Question

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

Answer 1

To rotate a point \((x, y)\) about the origin by 270 degrees counterclockwise, you can use the following transformation rule:

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

Now, apply this rule to the point \(M(0, 4)\):

1. Identify the coordinates of M:
\(x = 0\) and \(y = 4\).

2. Apply the rotation formula:
\[
M' = (y, -x) = (4, -0) = (4, 0)
\]

Thus, the image of point \(M\) after a 270-degree counterclockwise rotation about the origin is:

\[
M' = (4, 0)
\]