Question

1 triangle xyz is translated 4 units to the left and then rotated 90° counterclockwise about the point (1,1). what will be the coordinate pair for point x ? a (-3, -2) b (1, 2) c (-2, 5) d (5, 2)

Explanation:

Step1: Identify original X coordinate

Original point $X$ is at $(2,5)$.

Step2: Translate left 4 units

Subtract 4 from the x-coordinate: $2 - 4 = -2$. The translated point $X'$ is $(-2,5)$.

Step3: Shift to origin relative to (1,1)

Subtract $(1,1)$ from $X'$: $(-2 -1, 5 -1) = (-3,4)$.

Step4: 90° CCW rotation

Apply rotation formula $(x,y) \to (-y,x)$: $(-4,-3)$.

Step5: Shift back to original center

Add $(1,1)$ to the rotated point: $(-4 +1, -3 +1) = (-3,-2)$.

Answer:

A. $(-3,-2)$