Question

1. a rectangle is plotted on the grid to the right. which image shows a 90° clockwise rotation about the origin?
2. point a(-2, -10) is reflected over the x - axis. what are the coordinates of a?

a. (-2, -10) b. (2, 10) c. (-2, 10) d. (2, -10)

1. describe the transformation done on δrts to form δvxw

a. rotation around the origin 180°
b. reflection over the x - axis
c. reflection over the y - axis
d. translation

1. δqrs is translated 4 units left and 4 units up. how do the x - coordinates of the vertices change?

a. the x - coordinates increase by 4 because 4 is a positive number.
b. the x - coordinates decrease by 4 because “left” indicates a negative change.
c. the x - coordinates decrease by 4 because 4 is a positive number.
d. the x - coordinates increase by 4 because “left” indicates a positive change.
bonus solve: x - 1 = 5x + 3x - 8

Explanation:

Step1: Recall rotation rule

For a 90 - degree clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$. Analyze the rectangle's vertices transformation to find the correct image. (Since no specific rectangle vertices are given, we rely on general knowledge of 90 - degree clockwise rotation appearance).

Step2: Recall reflection rule

When a point $(x,y)$ is reflected over the $x$ - axis, the transformation rule is $(x,-y)$. For point $A(-2,-10)$, applying the rule gives $A'(-2,10)$.

Step3: Analyze triangle transformation

For two triangles $\triangle RTS$ and $\triangle VXW$, if we compare their orientations and positions, a 180 - degree rotation around the origin changes the sign of both $x$ and $y$ coordinates of all vertices. By observing the triangles' relative positions, we can determine the transformation.

Step4: Understand translation rule

For a translation 4 units left and 4 units up, the rule for a point $(x,y)$ is $(x - 4,y + 4)$. So the $x$ - coordinates of the vertices decrease by 4 because moving left on the $x$ - axis is a negative change.

Step5: Solve the equation

Combine like - terms on the right side of the equation $x−1 = 5x+3x−8$. The right side simplifies to $8x−8$. So we have $x−1=8x - 8$. Subtract $x$ from both sides: $-1 = 7x-8$. Then add 8 to both sides: $7 = 7x$. Divide both sides by 7 to get $x = 1$.

Answer:

1. (No specific answer as no original rectangle vertices are given to check against options)
2. C. $(-2,10)$
3. A. Rotation around the origin $180^{\circ}$
4. B. The $x$-coordinates decrease by 4 because “left” indicates a negative change.
5. $x = 1$