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A rotation by 90^(∘) clockwise ends up in the same place as a rotation by 270^(∘) counterclockwise.
F
We want to rotate trapezoid KLMN 90^(∘) clockwise about the origin. Let's look at the graph to identify the coordinates of vertices.
A rotation is a transformation about a point called center of rotation. Each point of the original figure and its image are the same distance from the center of rotation. When a counterclockwise rotation is performed about the origin, the coordinates of the image can be written in relation to the coordinates of the preimage.
| Rotations About the Origin | ||
|---|---|---|
| 90^(∘) Rotation | 180^(∘) Rotation | 270^(∘) Rotation |
|
ccc Preimage & & Image [0.5em] (x,y) & → & (- y,x) |
ccc Preimage & & Image [0.5em] (x,y) & → & (- x,- y) |
ccc Preimage & & Image [0.5em] (x,y) & → & (y,- x) |
We want to rotate a trapezoid 90^(∘) clockwise about the origin. A rotation by 90^(∘) clockwise ends up in the same place as a rotation by 270^(∘) counterclockwise. Therefore, we can use the coordinate changes shown in the table that correspond to a 270^(∘) clockwise to determine the coordinates of the image of each vertex. ccc Preimage & & Image (x,y) & → & (y, - x) [0.5em] K(1,- 1) & & K'(- 1,- 1) [0.5em] L(4,- 1) & & L'(- 1,- 4) [0.5em] M(2, - 3) & & M'(- 3,- 2) [0.5em] N(1,- 3) & & N'(- 3, - 1) We can see that coordinates of point M' are (- 3, - 2). That corresponds to option F.