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

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), using the rule $(x,y)\to(y, - x)$, we substitute $x = 6$ and $y = 3$. So the pre - image of A' is $(3,-6)$.

Step3: Find pre - image of B'

For point B'(-2, 1), substituting $x=-2$ and $y = 1$ into the rule $(x,y)\to(y, - x)$, we get the pre - image $(1,2)$.

Step4: Find pre - image of C'

For point C'(1, 7), substituting $x = 1$ and $y = 7$ into the rule $(x,y)\to(y, - x)$, we get the pre - image $(7,-1)$.

Answer:

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