Question

triangle xyz has vertices x(1, -1), y(3, 4), and z(5, -1). nikko rotated the triangle 90° counterclockwise about the origin. what is the correct set of image points for triangle x’y’z’?

○ x’(1, 1), y’(-4, 3), z’(1, 5)
○ x’(1, 1), y’(-3, -4), z’(-1, -5)
○ x’(-1, 1), y’(-3, -4), z’(-5, 1)
○ x’(-1, -1), y’(4, -3), z’(-1, -5)

Explanation:

Step1: Recall 90° counterclockwise rule

A point $(x,y)$ rotated 90° counterclockwise about the origin transforms to $(-y,x)$.

Step2: Apply rule to $X(1,-1)$

Substitute $x=1, y=-1$: $(-(-1),1)=(1,1)$

Step3: Apply rule to $Y(3,4)$

Substitute $x=3, y=4$: $(-4,3)$

Step4: Apply rule to $Z(5,-1)$

Substitute $x=5, y=-1$: $(-(-1),5)=(1,5)$

Answer:

$X'(1, 1), Y'(-4, 3), Z'(1, 5)$