Two triangles are drawn on a coordinate plane. The first triangle is labeled preimage and is drawn with a solid line in quadrant 1. The second triangle is labeled image and is drawn with a dotted line in quadrant 3.

Question

Examine the rotation to identify the center of rotation.

(1 point)
Responses

(0,1)
left parenthesis 0 comma 1 right parenthesis

(0,−1)
left parenthesis 0 comma negative 1 right parenthesis

(0,0)
left parenthesis 0 comma 0 right parenthesis

(1,0)

Answer 1

To determine the center of rotation between the preimage triangle in quadrant 1 and the image triangle in quadrant 3, we should first observe how the triangles are positioned.

When a shape is rotated, its points will shift in a circular path around the center of rotation. If a triangle in quadrant 1 (where both x and y coordinates are positive) is rotated to quadrant 3 (where both x and y coordinates are negative), then the center of rotation is likely at the origin (0,0).

Rotating about the origin would move points from the first quadrant (positive x, positive y) to the third quadrant (negative x, negative y).

Therefore, the center of rotation is:

(0,0)