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? a b c (-7, -1) (-1, -7) (1, -7) (7, -1)

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 reverse this rule. So, if $(x',y')$ is the image after 90 - degree rotation, the pre - image $(x,y)$ has coordinates $(y', - x')$.

Step2: Find pre - image of A'

For point A'(6, 3), using the rule $(y', - x')$, we get the pre - image A as (3, - 6).

Step3: Find pre - image of B'

For point B'(-2, 1), using the rule $(y', - x')$, we get the pre - image B as (1, 2).

Step4: Find pre - image of C'

For point C'(1, 7), using the rule $(y', - x')$, we get the pre - image C as (7, - 1).

Answer:

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