Question

1. which transformation would take shape a to shape b? a. a counterclockwise rotation of 90° about the origin b. a reflection over the line y = x c. a reflection over the line y = -x d. a counterclockwise rotation of 180° about the origin 2. which transformation would take shape a to shape b? a. a clockwise rotation of 90° about the origin b. a reflection over the x - axis c. a clockwise rotation of 270° about the origin d. a reflection over the y - axis 3. which transformation would take shape a to shape b? a. a counterclockwise rotation of 90° about the origin b. a reflection over the line y = -x c. a reflection over the line y = x d. a counterclockwise rotation of 180° about the origin 4. which transformation would take shape a to shape b? a. a counterclockwise rotation of 90° about the origin b. a reflection over the x - axis c. a reflection over the y - axis d. a counterclockwise rotation of 270° about the origin

Explanation:

Question 1

Step1: Recall rotation and reflection rules

For a point $(x,y)$: a counter - clockwise rotation of $90^{\circ}$ about the origin gives $(-y,x)$; a reflection over $y = x$ gives $(y,x)$; a reflection over $y=-x$ gives $(-y,-x)$; a counter - clockwise rotation of $180^{\circ}$ about the origin gives $(-x,-y)$. By observing the orientation and position of Shape A and Shape B, we can see that a reflection over the line $y = -x$ maps Shape A to Shape B.

Step1: Recall transformation rules

For a point $(x,y)$: a clockwise rotation of $90^{\circ}$ about the origin gives $(y, - x)$; a reflection over the $x$ - axis gives $(x,-y)$; a clockwise rotation of $270^{\circ}$ about the origin gives $(-y,x)$; a reflection over the $y$ - axis gives $(-x,y)$. By observing the orientation and position of Shape A and Shape B, we can see that a reflection over the $x$ - axis maps Shape A to Shape B.

Step1: Recall transformation rules

For a point $(x,y)$: a counter - clockwise rotation of $90^{\circ}$ about the origin gives $(-y,x)$; a reflection over the line $y=-x$ gives $(-y,-x)$; a reflection over the line $y = x$ gives $(y,x)$; a counter - clockwise rotation of $180^{\circ}$ about the origin gives $(-x,-y)$. By observing the orientation and position of Shape A and Shape B, we can see that a counter - clockwise rotation of $90^{\circ}$ about the origin maps Shape A to Shape B.

Answer:

C. A reflection over the line $y=-x$

Question 2