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 $A'(6,3)$, using the rule $(x,y)\to(y, - x)$, we get $A(3,-6)$.

Step3: Find pre - image of $B'$

For $B'(-2,1)$, using the rule $(x,y)\to(y, - x)$, we get $B(1,2)$.

Step4: Find pre - image of $C'$

For $C'(1,7)$, using the rule $(x,y)\to(y, - x)$, we get $C(7,-1)$.

Answer:

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