Question

A quadrilateral with vertices G(−10,1) , E(−6,−4) , O(2,0) , and M(0,4) is rotated about the origin 270 degrees (counterclockwise). Apply rotation mapping rules to find the image of M.(1 point)
Responses

M'( -4, 0)
M'( -4, 0)

M'( 0, 4)
M'( 0, 4)

M'( 4, 0)
M'( 4, 0)

M'( 0, -4)

Answer 1

To rotate a point \((x, y)\) about the origin by 270 degrees counterclockwise, we can use the rotation mapping rules. The formula for a 270-degree counterclockwise rotation is:

\[
(x, y) \rightarrow (y, -x)
\]

For point \(M(0, 4)\):

1. According to the rotation rule, we replace \(x\) with \(0\) and \(y\) with \(4\):
\[
(0, 4) \rightarrow (4, 0)
\]

So, the image of point \(M\) after a 270-degree rotation about the origin will be:

\[
M' (4, 0)
\]

Thus, the correct response is:

**M'(4, 0)**.