Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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section b 10 marks answer one question from this section 1 find the len…
\(\sqrt{21}\) ### Question 2: Find the equation of the parabola having its vertex at the origin and symmetrical about the \(x\)-axis and passing through the point \((-4,-10)\)
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work: section 1.3 homework question 14, 1.3.63 part 1 of 3 hw score: 63…
\(x^2 + y^2 = 16\)
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for the figure, do a dilation centered at the origin with a scale facto…
8
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write the standard equation for each of the circles in parts (a) throug…
(for part b): \(x^2 + y^2 = 26\) (Note: For part (a), the equation is already given as \(x^2 + y^2 = 9\), which is the standard form with center \((0,0)\) and radius \(3\).)
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write the standard equation for each of the circles in parts (a) throug…
(for part b): The equation of the circle in standard form is \(\boldsymbol{(x - 3)^2 + y^2 = 4}\) (or if we expand to \(x^2 + y^2\) form: \(x^2 + y^2=6x - 5\), but the standard fo…
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(a) the arrows below show that the coordinates on the left are mapped t…
### Part (a) #### Step 1: Analyze the rotation for point \( E \) Original coordinates of \( E \) are \( (2, 1) \). Let's assume the rotation rule (we can check with part (b) later…
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1.3 homework question 14, 1.3.63 part 2 of 3 hw score: 81.9%, 13 of 21 …
(for part a correction): \(x^2 + y^2 = 49\)
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(a) the equation of the circle in standard form is ( x^2 + y^2 = 49 ) (…
\((x - 5)^2+y^2=4\)
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write the standard equation for each of the circles in parts (a) throug…
\(x^2 + y^2 = 49\)
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determine the center and radius of the following circle and sketch the …
The center of the circle is \((3,-4)\) and the radius is \(5\) (since \(r^{2}=25\), so \(r = 5\)).
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bertie placed a transparent grid made up of unit squares over each of t…
a. $\boxed{16}$ b. $\boxed{16}$
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5. the perimeter of the triangle at right is 52 units. write and solve …
The value of \(x\) is \(2\). The side lengths of the triangle are \(10\) units, \(23\) units, and \(19\) units.
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1-64. decide which transformation was used on each pair of shapes below…
### Part a # Explanation: ## Step1: Analyze shape a's transformation The two shapes in part a seem to be mirror images or related by a reflection (or could also be a rotation, but…
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use the figure below for problem 7 below and 8 – 10 on the back. $overl…
x = 8, AC = 30 ### Problem 8
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which of the following statements about parallel and perpendicular line…
The correct statement is the one in the orange box: "Parallel lines never meet and stay the same distance apart, while perpendicular lines meet at a right angle"
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the following statement describes a ladder. based only on the statement…
B. Using the Perpendicular Transversal Theorem and the fact that the side is a traversal perpendicular to the top rung and all rungs are parallel, the conclusion is that all the r…
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which type of transformation takes triangle a to triangle b? image: gri…
Reflection
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the distinct lines a, b, c, and d are in the same plane. draw a diagram…
(Diagram) D (Relationship) C. The line a is perpendicular to d because a is perpendicular to b, b is parallel to c, and c is parallel to d.
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find the measure of each angle. 3x + 8 37x + 2 3x + 8 = □° 37x + 2 = □°…
\( 3x + 8 = 14^\circ \) \( 37x + 2 = 76^\circ \) (Step-by-step explanation: The two angles form a right angle, so their sum is \( 90^\circ \). \( (3x + 8) + (37x + 2) = 90 \) \( 4…
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spiral review identify which figures are a reflection of figure a, and …
First box: Figure 4 is Second box: Figure 1 is
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spiral review a figure has two pairs of parallel sides and four right a…
2
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test prep a pentagon has vertices at $(-1, -1)$, $(-5, -2)$, $(-6, -4)$…
\((1, 1)\), \((5, 2)\), \((6, 4)\), \((4, 7)\), \((2, 3)\)
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supply the missing reasons in the two-column proof. given: a || b, c ||…
2) Alternate Interior Angles Theorem (or Corresponding Angles Theorem, depending on the position; since \(a \parallel b\) and \(c\) is a transversal, \(\angle 3\) and \(\angle 2\)…
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constructing parallel and perpendicular lines which statement is true f…
A. Parallel lines have the same slope.
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identify one of the steps necessary to construct a parallel line to a g…
B. With the pointed tip of your compass on a point on the given line, draw an arc that intersects the given line and the line drawn from the point on the given line to the point n…
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find the value of the variable. the value of p is \\(\\square\\). (simp…
27 To find the value of \( p \), we note that the angle \( (4p - 18)^\circ \) is a right angle (since the lines are perpendicular, indicated by the right angle symbol). A right an…
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determine the intercepts of the line. x-intercept: ( , ) y-intercept: (…
x - intercept: \((-1, 0)\) y - intercept: \((0, 4.5)\) Wait, no, looking at the graph again, the vertical axis is labeled x, with x from 1 to 8, and horizontal axis labeled y, wit…
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test prep what rotation of △mnp about point p could have produced △pqr …
\(180^\circ\) clockwise
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test prep rotate the parallelogram 90° counterclockwise about the origi…
The rotated parallelogram has vertices at \((-5, 1)\), \((-2, 1)\), \((0, 3)\), and \((-3, 3)\) (plotted using the Polygon Tool as per the rotation rule).
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identify which diagram represents a step in constructing a perpendicula…
(Assuming the correct diagram is one where the perpendicular line does not pass through the midpoint of the segment. Since the given diagram is a perpendicular bisector, the corre…
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lesson 2 cool-down the side lengths of rectangles 1. what are all of th…
The possible side - length pairs (length, width) of the rectangle with an area of 21 square units are \( (1, 21) \), \( (3, 7) \), \( (7, 3) \) and \( (21, 1) \). If we consider n…
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constructing parallel and perpendicular lines quick check select the ch…
\(\boldsymbol{\overline{AB} \perp \overline{CD}}\) and \(\boldsymbol{\overline{CP} \cong \overline{DP}}\) (the last option)
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describe the rotation in mapping notation. enter the correct answer in …
\((x, y) \to (-y, x)\) (So the first box is \(-y\) and the second is \(x\))
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constructing parallel and perpendicular lines quick check when performi…
D. a compass and a straightedge
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question what is the image of (12,4) after a dilation by a scale factor…
\((3, 1)\)
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bernie is practicing the 100-meter dash on the straight portion of his …
The second graph (the one with the triangle - shaped line starting at the origin, going up to a peak, then down to the x - axis) shows Bernie's distance from the starting line ove…
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what is the image of (-12, -4) after a dilation by a scale factor of \\…
\((-3, -1)\)
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geometry basics > constructing parallel and perpendicular lines image l…
\( \perp \)
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4. list two triangles whose lengths can be represented by the equivalen…
One triangle has side lengths \(4\), \(5\), \(3\) and another triangle has side lengths \(8\), \(10\), \(6\) (other valid similar triangles can also be formed by scaling these sid…
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question what is the image of (0, 4) after a dilation by a scale factor…
\((0, 12)\)
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to place each of the described points on the numbered line. 2/7 of the …
First point: -32 Second point: 16
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question what is the image of (-3, 0) after a dilation by a scale facto…
\((-1, 0)\)
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the table shows the steps for constructing a parallel line to a given l…
3 (Note: The exact step number depends on the full list of steps, but based on standard parallel line construction, this step (copying the arc/angle with compass) is typically a m…
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12. chris wants to reduce a triangular pattern with sides 16, 16, and 2…
The other two sides should each be 12 centimeters.
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find the value of x for which d||m. (2x−27)° 87° d m x=□ (simplify your…
To determine the value of \( x \) for which \( d \parallel m \), we use the property of alternate interior angles (or corresponding angles, depending on the configuration). When t…
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3. for each scaled copy, write the scale factor that takes triangle t t…
To solve for the scale factor of each triangle (assuming Triangle \( T \) has sides, let's first identify the sides of Triangle \( T \). Wait, maybe Triangle \( T \) is one of the…
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question what is the image of (4,6) after a dilation by a scale factor …
\((8, 12)\)
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name lesson 1 cool-down area and multiples if a rectangle is 6 tiles wi…
If the rectangle has a width of 6 tiles, and let the length be \( l \) tiles, the area \( A = 6l \). For example, if \( l = 7 \), \( A=6\times7 = 42 \) square tiles; if \( l = 6 \…
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2. identify the missing information from the 2 - column proof. diagram:…
\( \angle G \cong \angle D \) (the option with \( \angle G \cong \angle D \))
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11. a telephone booth that is 8 ft tall casts a shadow that is 4 ft. lo…
The scale factor is 2 and the height of the lawn ornament is 4 ft.
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2. identify the missing information from the 2 - column proof. statemen…
\(\boldsymbol{\angle G\cong\angle D}\) (corresponding to the option with \(\angle G\cong\angle D\) in the multiple - choice options)
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1. what information could not be used to prove the congruence of the tr…
$\boldsymbol{\angle A\cong\angle D}$
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lesson #1 1. circle the number that is greater 8 (with 8 green circles)…
Circle the number 8. ### Problem 2: Number of cents (penny)
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solve the inequality and graph the solution. ( 4 < \frac{b}{2} + 8 ) to…
The solution to the inequality is \( b > - 8 \). To graph this, we plot an open circle at \( - 8 \) (since the inequality is strict, \( b eq - 8 \)) and draw an arrow to the righ…
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what is the image of (9, -4) after a dilation by a scale factor of 5 ce…
\( (45, -20) \)
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solve the inequality and graph the solution. ( 1 leq \frac{n + 4}{6} ) …
The solution to the inequality is \(n \geq 2\). For the graph, plot a closed circle at \(2\) on the number line and draw an arrow to the right.
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level 3 tweety name bernard holding the paper vertically, plot each poi…
To complete the task, follow these steps: 1. Draw a coordinate plane with x - axis (horizontal) and y - axis (vertical), origin at \((0,0)\), positive x to the right, negative x t…
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a, b, and c are the centers of the 3 circles. select all the segments t…
A. \( HF \), B. \( HA \), D. \( CD \), E. \( BD \), F. \( BF \)
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question what is the image of (2, -7) after a dilation by a scale facto…
\( (8, -28) \)
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10. a photograph measuring 4 inches wide, and 5 inches long is enlarged…
The length of the mural is 15 inches.
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find the value of x that makes m||n. x = \\boxed{\\quad} (simplify your…
\( x = 39 \)
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complete the following statement by entering the correct number associa…
3. perpendicular
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f is a point on segment \\( \\overline{eg} \\). if \\( ef = 5x \\), \\(…
\( 16 \)
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solve the inequality and graph the solution. 6r + 4 > 16 to draw a ray,…
The solution to the inequality \( 6r + 4 > 16 \) is \( r > 2 \). To graph it, plot an open circle at \( 2 \) on the number line and draw an arrow to the right.
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v is a point on segment (overline{uw}). if (uv = 13), (vw = x + 15), an…
31
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solve the inequality and graph the solution. 1 ≤ -5 + 3q to draw a ray,…
The solution to the inequality \( 1\leq5 + 3q \) is \( q\geq-\frac{4}{3} \). For the graph, plot a closed circle at \( -\frac{4}{3} \) (or approximately - 1.33) on the number line…
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on a line segment, u is between t and v. if tu = x + 9, uv = 6, and tv …
11
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si el jardín tiene una profundidad de 0.5 metros, ¿cuál es el volumen d…
\(6 \, m^3\)
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solve the inequality and graph the solution. 6 ≤ 3(h − 2) to draw a ray…
The solution to the inequality \( 6 \leq 3(h - 2) \) is \( h \geq 4 \). To graph it, plot a closed circle at \( 4 \) on the number line and draw an arrow to the right.
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four quadrant ordered pairs tell what point is located at each ordered …
### Part 1: Identify Point from Ordered Pair To solve, we use the coordinate grid: the first number is the \( x \)-coordinate (horizontal), the second is the \( y \)-coordinate (v…
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tu jardín mide 6 metros de largo y 4 metros de ancho. ¿cuál es el área …
24 \( m^2 \) (corresponding to the option with \( 24 \, m^2 \))
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u is a point on segment (overline{tv}). if (tu = 6x + 10), (uv = 4x), a…
118
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cfu midpoint and fractional distance checkpoint - due 9/9/25 (-10 each …
- Midpoint of \( \overline{RM} \): \( 2 \) - Midpoint of \( \overline{QP} \): \( -2 \) - Midpoint of \( \overline{MP} \): \( 28 \)
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a triangle has vertices at (-3, 4), (-1, 0), and (-4, 0). what are the …
\((3, -4)\), \((1, 0)\), \((4, 0)\)
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if bc = 6x, cd = x + 8, and bd = 15, what is bc? simplify your answer a…
6
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use the image to answer the question image long description based on th…
For \( l\square\overline{XY} \), the symbol is \( \perp \); for \( XP\square PY \), the symbol is \( = \).
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if bc = x + 10, cd = 7x - 2, and bd = 16, what is cd? diagram: line seg…
5
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solve the inequality and graph the solution. $9 < \\frac{w}{-2} + 8$ to…
The solution to the inequality is \( w < -2 \). To graph this, we plot an open circle at -2 (since the inequality is strict, \( w eq -2 \)) and draw an arrow to the left (indica…
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if pq = 4x, qr = x + 3, and pr = 6x − 5, what is pr? diagram: p---q---r…
43
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a rectangle that is 2 inches by 3 inches has been scaled by a factor of…
The side lengths of the scaled copy are 14 inches and 21 inches.
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find the distance between the points. (4,5) and (-2,5) the distance is …
6
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if kl = 8x, lm = 16x − 6, and km = 18, what is kl? simplify your answer…
8
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solve the inequality and graph the solution. \\(\frac{w}{-1} + 8 < 4\\)…
The solution to the inequality is \( w>4 \). To graph this, we plot an open circle at 4 (since the inequality is strict, \( w eq4 \)) and draw an arrow to the right (indicating a…
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solve the inequality and graph the solution. \\( \\frac{u}{-6} + 7 > 6 …
The solution to the inequality \(\frac{u}{-6}+7 > 6\) is \(u < 6\). To graph this solution: 1. On the number line, plot an open circle at \(u = 6\) (since the inequality is strict…
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if pq = 7x, qr = 13x − 4, and pr = 19x + 15, what is pr? diagram of lin…
376
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part b list the coordinates of the vertices of the rotated rectangle. e…
\((1, 5)\), \((3, 6)\), \((5, 2)\), \((3, 1)\)
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part b list the coordinates of the vertices of the rotated rectangle. e…
To solve for the coordinates of the vertices of the rotated rectangle, we typically need the original coordinates of the rectangle's vertices and the angle of rotation (or other r…
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if uv = 13x, vw = 9x − 15, and uw = 20x + 19, what is uv? diagram: u---…
221
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8. scale factor= ______ missing side length =______
Scale Factor = \(\frac{2}{3}\) Missing Side length = \(10\)
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8. image of two triangles (one with vertices a, b, c, right angle at b,…
Scale Factor = \(\frac{2}{3}\) Missing Side length = \(10\)
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7. scale factor= ____ missing side length = ____
Scale Factor = $\frac{3}{4}$, Missing Side length = 15
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part a graph rectangle (abcd). then draw a rotation of the rectangle (9…
To solve the problem, follow these steps: 1. **Identify Original Vertices**: From the graph, the vertices of Rectangle \(ABCD\) are approximately \((1, 5)\), \((3, 6)\), \((3, 1)\…
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6. scale factor= ______ missing side length =______
Scale Factor = $\frac{1}{2}$ Missing Side length = 4
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given: qr = 59; rt = 59 prove: qr = rt | statements | reason | | --- | …
Transitive Property of Equality
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given: ab = 3x + 2; bc = 4x + 8; ac = 38 prove: x = 4 | statements | re…
line 2
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name the figure below in two different ways. symbol: and
$\overrightarrow{QB}$ and $\overrightarrow{QE}$ (or alternatively, if the ray is considered to start at Q and the direction is towards B, another way could be named as Ray QB and …
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double-angle formulas find the value of \\( \\sin 2\\theta \\) given \\…
145
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for u.s. businesses with strong export capabilities, expansion of u.s. …
B. opportunities (assuming the second option is labeled B; if the original labels are different, adjust accordingly, e.g., if the "opportunities" option is the second circle, then…
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find the m∠bac, if m∠dec = 58° and m∠edc = 43°. options: 79°, 101°, 58°…
\(79^\circ\)
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important! angles must belong to the same transversal to be an angle pa…
To solve for each angle pair, we analyze their positions relative to the transversals (lines \(a\), \(b\), and \(d\)): ### Part e: \(\angle 4\) and \(\angle 7\) - **Step 1**: Iden…