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) M′ (,)

Answer 1

To rotate a point counterclockwise about the origin by an angle of 270 degrees, we can use the following rotation mapping rule:

(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)

where (x, y) is the original point, (x', y') is the new image point, and θ is the angle of rotation.

In this case, the original point M is (0, 4) and the angle of rotation is 270 degrees.

Using the rotation mapping rule:

(x', y') = (0*cos270 - 4*sin270, 0*sin270 + 4*cos270)
= (0 - (-4), 0 + 0)
= (4, 0)

Therefore, the image of M is M' (4, 0).

Answer 2

A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? Enter the number of the correct option. Option #1: (x,y)→(y,−x) Option #2: (x,y)→(−y,x) Option #3: (x,y)→(−x,−y) Option #4: (x,y)→(y,x) (1 point) The mapping for a 90-degree counterclockwise rotation is Option #.