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 reverse this rule. So, if the image point is $(x,y)$, the pre - image point is $(y, - x)$.

Step2: Find pre - image of $A'$

For $A'(6,3)$, using the reverse rule $(y, - x)$, the pre - image point $A$ has coordinates $(3,-6)$.

Step3: Find pre - image of $B'$

For $B'(-2,1)$, the pre - image point $B$ has coordinates $(1,2)$.

Step4: Find pre - image of $C'$

For $C'(1,7)$, the pre - image point $C$ has coordinates $(7,-1)$.

Answer:

The coordinates of the pre - image vertices are $A(3,-6)$, $B(1,2)$, $C(7,-1)$