A quadrilateral with vertices G(−10,1)

Question

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:

$$(x,y)\to (y,-x)$$

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: $$M^{\prime }=(y,-x)=(4,-0)=(4,0)$$

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

$$M^{\prime }=(4,0)$$