Question

The vertices of a triangle are A(-4,1), B(-2, 2), and C(-1, 1). Rotate the triangle as described. Find the coordinates of the image.

270° clockwise about the origin
90° counterclockwise about the origin
180° about the origin
90° clockwise about

Answer 1

To find the new coordinates of a triangle's vertices after rotation, apply the transformations for 90° clockwise, 90° counterclockwise, and 180° rotations around the origin to each vertex.

Step-by-step explanation:

The question asks for the coordinates of a triangle's vertices after various rotations around the origin. To rotate a point (x,y) around the origin:

• For a 90° clockwise rotation, the new coordinates become (y, -x).
• For a 90° counterclockwise rotation, the new coordinates become (-y, x).
• For a 180° rotation, the new coordinates become (-x, -y).

Now, applying these transformations to the given vertices:

• For A(-4,1), the 90° clockwise rotation gives A'(1, 4), the 90° counterclockwise rotation gives A'(-1, -4), and the 180° rotation gives A'(4, -1).
• For B(-2,2), the 90° clockwise rotation gives B'(2, 2), the 90° counterclockwise rotation gives B'(-2, -2), and the 180° rotation gives B'(2, -2).
• For C(-1,1), the 90° clockwise rotation gives C'(1, 1), the 90° counterclockwise rotation gives C'(-1, -1), and the 180° rotation gives C'(1, -1).