Question

a rectangle was rotated 270° about the origin. the image is shown. which points are vertices of the pre - image? check all that apply. k(-3, -1) m(-3, 2) m(3, 2) n(-3, 1) n(3, 1)

Explanation:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 270° counter - clockwise about the origin is $(x,y)\to(y, - x)$.

Step2: Identify vertices of image

From the graph, assume the vertices of the image rectangle are $K'(1, - 3)$, $L'(2,-3)$, $M'(2, - 4)$, $N'(1,-4)$.

Step3: Apply inverse rotation rule

To find the pre - image vertices, we use the inverse rule $(x,y)\to(-y,x)$.
For a point $(x,y)$ of the image, the pre - image point $(x_{pre},y_{pre})$ has $x_{pre}=-y$ and $y_{pre}=x$.
For $K'(1, - 3)$, the pre - image $K(-3,1)$.
For $L'(2,-3)$, the pre - image $L(-3,2)$.
For $M'(2, - 4)$, the pre - image $M(-4,2)$.
For $N'(1,-4)$, the pre - image $N(-4,1)$.
Among the given options, the correct pre - image vertices are:

Answer:

M(-3,2)