Question

1. figure u is the result of a transformation on figure t. which transformation would accomplish this? a. a rotation 90° counterclockwise about the origin b. a reflection over the y -axis c. a rotation 90° clockwise about the origin d. a reflection over the x -axis

Explanation:

Step1: Recall transformation rules

For a 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$. For a reflection over the y - axis, the rule is $(x,y)\to(-x,y)$. For a 90 - degree clockwise rotation about the origin, the rule is $(x,y)\to(y, - x)$. For a reflection over the x - axis, the rule is $(x,y)\to(x,-y)$.

Step2: Check key points

Let's take a key point on Figure T, say $(3, - 3)$.
If we perform a 90 - degree counter - clockwise rotation about the origin on the point $(3,-3)$ using the rule $(x,y)\to(-y,x)$, we get $(3,3)$.
If we perform a reflection over the y - axis on the point $(3,-3)$ using the rule $(x,y)\to(-x,y)$, we get $(-3,-3)$.
If we perform a 90 - degree clockwise rotation about the origin on the point $(3,-3)$ using the rule $(x,y)\to(y,-x)$, we get $(-3,-3)$.
If we perform a reflection over the x - axis on the point $(3,-3)$ using the rule $(x,y)\to(x,-y)$, we get $(3,3)$.
By observing the orientation and position of Figure U relative to Figure T, we can see that a 90 - degree counter - clockwise rotation about the origin maps Figure T to Figure U.

Answer:

A. A rotation 90° counterclockwise about the origin