Question

after a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are a(6, 3), b(-2, 1), and c(1, 7). what are the coordinates of the vertices of the pre - image?

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. To find the pre - image, we use the reverse rule $(x,y)\to(y, - x)$.

Step2: Find pre - image of A'

For point A'(6,3), applying the reverse rule: $x = 6,y = 3$, so the pre - image A is $(3,-6)$.

Step3: Find pre - image of B'

For point B'(-2,1), applying the reverse rule: $x=-2,y = 1$, so the pre - image B is $(1,2)$.

Step4: Find pre - image of C'

For point C'(1,7), applying the reverse rule: $x = 1,y = 7$, so the pre - image C is $(7,-1)$.

Answer:

A. (3,-6)
B. (1,2)
C. (7,-1)