Question

if the image of m after a 90 counterclockwise rotation about the origin is m(-4,3), what is the preimage m? (3,4) (-3,-4) (4,-3) (-4,3)

Explanation:

Step1: Recall rotation rule

The rule for a 90 - counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. Let the pre - image $M$ be $(x,y)$ and the image $M'$ be $(-4,3)$.

Step2: Apply the inverse rule

If $(-y,x)=(-4,3)$, then we can solve the system of equations

$$\begin{cases}-y = - 4\\x = 3\end{cases}$$

. From $-y=-4$, we get $y = 4$, and $x = 3$. So the pre - image $M$ is $(3,4)$.

Answer:

$(3,4)$