20. give the image coordinate using the appropriate notation. state the rule.
a (7,3) translate 4 left and 8 down
rule:

b (-2, -8) rotate 90° ccw
rule: -y, x

c (-1,7) translate 2 up and 6 right
rule:

d (-5,4) rotate 90° cw
rule: y, -x

e (-9, -8) reflect over the x - axis
rule: x, -y

f (6,2) rotate 180° ccw
rule: -x, -y

g (-7,1) reflect over the y - axis
rule: -x, y

h (-6,9) dilate by a scale factor of 2
rule:

21. which statement is true? (preserves - does not change; it stays the same)
a. reflections will preserve the figure’s side lengths but will not preserve the angle measurements
b. reflections will not preserve the figure’s side lengths but will preserve the angle measurements
c. dilations will preserve the figure’s side lengths and will not preserve the angle measurements
d. dilations will not preserve the figure’s side lengths but will preserve the angle measurements

22. which of the following must be true?
a. f = u + n
b. f + n = a
c. u + n + b = 180
d. u + n = b
(there is a triangle - related image on the right with angles labeled f, u, n and points a, b)

23. write each decimal as a fraction in lowest terms
0.24
\frac{24}{100}
0.242424...

Question

20. give the image coordinate using the appropriate notation. state the rule.
a (7,3) translate 4 left and 8 down
rule:

b (-2, -8) rotate 90° ccw
rule: -y, x

c (-1,7) translate 2 up and 6 right
rule:

d (-5,4) rotate 90° cw
rule: y, -x

e (-9, -8) reflect over the x - axis
rule: x, -y

f (6,2) rotate 180° ccw
rule: -x, -y

g (-7,1) reflect over the y - axis
rule: -x, y

h (-6,9) dilate by a scale factor of 2
rule:

21. which statement is true? (preserves - does not change; it stays the same)
a. reflections will preserve the figure’s side lengths but will not preserve the angle measurements
b. reflections will not preserve the figure’s side lengths but will preserve the angle measurements
c. dilations will preserve the figure’s side lengths and will not preserve the angle measurements
d. dilations will not preserve the figure’s side lengths but will preserve the angle measurements

22. which of the following must be true?
a. f = u + n
b. f + n = a
c. u + n + b = 180
d. u + n = b
(there is a triangle - related image on the right with angles labeled f, u, n and points a, b)

23. write each decimal as a fraction in lowest terms
0.24
\frac{24}{100}
0.242424...

Accepted Answer

### Question 20 (Point A: Translate 4 left and 8 down)
# Explanation:
## Step1: Recall translation rule
For a translation of $ h $ units left/right and $ k $ units up/down, the rule is $(x,y)\to(x - h,y - k)$ (left is negative $ h $, down is negative $ k $). Here, $ h = 4 $ (left) and $ k = 8 $ (down).
## Step2: Apply to point A(7,3)
Substitute $ x = 7 $, $ y = 3 $, $ h = 4 $, $ k = 8 $ into the rule: $(7 - 4,3 - 8)=(3,-5)$.
# Answer: $(3, - 5)$, Rule: $(x,y)\to(x - 4,y - 8)$

### Question 20 (Point B: Rotate $ 90^\circ $ ccw)
# Explanation:
## Step1: Recall $ 90^\circ $ ccw rotation rule
The rule for $ 90^\circ $ counter - clockwise rotation is $(x,y)\to(-y,x)$.
## Step2: Apply to point B(-2,-8)
Substitute $ x=-2 $, $ y = - 8 $ into the rule: $(-(-8),-2)=(8,-2)$.
# Answer: $(8, - 2)$, Rule: $(x,y)\to(-y,x)$

### Question 20 (Point C: Translate 2 up and 6 right)
# Explanation:
## Step1: Recall translation rule
For a translation of $ h $ units right (positive $ h $) and $ k $ units up (positive $ k $), the rule is $(x,y)\to(x + h,y + k)$. Here, $ h = 6 $, $ k = 2 $.
## Step2: Apply to point C(-1,7)
Substitute $ x=-1 $, $ y = 7 $, $ h = 6 $, $ k = 2 $ into the rule: $(-1 + 6,7+2)=(5,9)$.
# Answer: $(5, 9)$, Rule: $(x,y)\to(x + 6,y + 2)$

### Question 20 (Point D: Rotate $ 90^\circ $ cw)
# Explanation:
## Step1: Recall $ 90^\circ $ cw rotation rule
The rule for $ 90^\circ $ clockwise rotation is $(x,y)\to(y,-x)$.
## Step2: Apply to point D(-5,4)
Substitute $ x=-5 $, $ y = 4 $ into the rule: $(4,-(-5))=(4,5)$.
# Answer: $(4, 5)$, Rule: $(x,y)\to(y,-x)$

### Question 20 (Point E: Reflect over the x - axis)
# Explanation:
## Step1: Recall x - axis reflection rule
The rule for reflection over the x - axis is $(x,y)\to(x,-y)$.
## Step2: Apply to point E(-9,-8)
Substitute $ x=-9 $, $ y = - 8 $ into the rule: $(-9,-(-8))=(-9,8)$.
# Answer: $(-9, 8)$, Rule: $(x,y)\to(x,-y)$

### Question 20 (Point F: Rotate $ 180^\circ $ ccw)
# Explanation:
## Step1: Recall $ 180^\circ $ rotation rule
The rule for $ 180^\circ $ counter - clockwise (or clockwise) rotation is $(x,y)\to(-x,-y)$.
## Step2: Apply to point F(6,2)
Substitute $ x = 6 $, $ y = 2 $ into the rule: $(-6,-2)$.
# Answer: $(-6, - 2)$, Rule: $(x,y)\to(-x,-y)$

### Question 20 (Point G: Reflect over the y - axis)
# Explanation:
## Step1: Recall y - axis reflection rule
The rule for reflection over the y - axis is $(x,y)\to(-x,y)$.
## Step2: Apply to point G(-7,1)
Substitute $ x=-7 $, $ y = 1 $ into the rule: $(-(-7),1)=(7,1)$.
# Answer: $(7, 1)$, Rule: $(x,y)\to(-x,y)$

### Question 20 (Point H: Dilate by a scale factor of 2)
# Explanation:
## Step1: Recall dilation rule
The rule for dilation with scale factor $ k $ is $(x,y)\to(kx,ky)$. Here, $ k = 2 $.
## Step2: Apply to point H(-6,9)
Substitute $ x=-6 $, $ y = 9 $, $ k = 2 $ into the rule: $(2\times(-6),2\times9)=(-12,18)$.
# Answer: $(-12, 18)$, Rule: $(x,y)\to(2x,2y)$

### Question 21
# Explanation:
- **Option A**: Reflections are rigid transformations. Rigid transformations preserve both side lengths and angle measurements. So, this statement is false.
- **Option B**: Reflections are rigid transformations, so they preserve both side lengths and angle measurements. This statement is false.
- **Option C**: Dilations are non - rigid transformations. They change the side lengths (scale them by a factor) but preserve the angle measurements. So, this statement is false.
- **Option D**: Dilations scale the side lengths (do not preserve them) but preserve the angle measurements. This statement is true.
# Answer: D. Dilations will not preserve the figure’s side lengths but will preserve the angle measurements

### Question 22
# Explanation:
We use the exterior angle theorem of a triangle, which states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the given triangle, $ \angle B $ is an exterior angle, and $ \angle U $ and $ \angle N $ are the two non - adjacent interior angles. So, $ U + N=B $.
- **Option A**: There is no such relationship based on the exterior angle theorem.
- **Option B**: There is no such relationship based on the exterior angle theorem.
- **Option C**: The sum of the interior angles of a triangle is $ 180^\circ $, but $ U + N + B$ is not the sum of interior angles.
- **Option D**: Follows the exterior angle theorem.
# Answer: D. $ U + N = B $

### Question 23 (0.24)
# Explanation:
## Step1: Write as a fraction
$ 0.24=\frac{24}{100} $
## Step2: Simplify the fraction
Find the greatest common divisor (GCD) of 24 and 100. The GCD of 24 and 100 is 4. Divide both the numerator and the denominator by 4: $ \frac{24\div4}{100\div4}=\frac{6}{25} $
# Answer: $ \frac{6}{25} $

### Question 23 (0.242424...)
# Explanation:
## Step1: Let $ x = 0.242424\cdots $
## Step2: Multiply by 100 (since the repeating cycle is 2 digits)
$ 100x=24.242424\cdots $
## Step3: Subtract $ x $ from $ 100x $
$ 100x - x=24.242424\cdots-0.242424\cdots $
$ 99x = 24 $
## Step4: Solve for $ x $
$ x=\frac{24}{99} $, simplify the fraction. The GCD of 24 and 99 is 3. Divide both numerator and denominator by 3: $ \frac{24\div3}{99\div3}=\frac{8}{33} $
# Answer: $ \frac{8}{33} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 20 (Point A: Translate 4 left and 8 down)

Step1: Recall translation rule

Step2: Apply to point A(7,3)

Step1: Recall \( 90^\circ \) ccw rotation rule

Step2: Apply to point B(-2,-8)

Step1: Recall translation rule

Step2: Apply to point C(-1,7)

Answer:

Question 20 (Point B: Rotate \( 90^\circ \) ccw)