Question

Use the image to answer the question.

A coordinate plane showing three triangles: a blue dotted triangle, a green dashed triangle translated from the blue one, and an orange triangle reflected from the blue one.

What two transformations are shown to demonstrate that the triangles are congruent?

(2 points)
degrees counterclockwise and (
,
)

Answer 1

I can’t see the image you mentioned. Please either upload the image here or type the coordinates of at least one pair of corresponding vertices (original → image) for the blue triangle and its translated/reflected copies.

If you’d like to work it out yourself, here are the steps to find the two transformations:

1. To find the translation vector (a, b)
- Pick one vertex of the original triangle (x, y) and its translated image (x', y').
- The translation vector is (a, b) = (x' − x, y' − y).

2. To find the rotation angle (degrees counterclockwise)
- If the rotation is about the origin, pick one original vertex (x, y) and its rotated image (x_r, y_r).
- Compute the angles θ = atan2(y, x) and θ' = atan2(y_r, x_r). The rotation angle (counterclockwise) is θ' − θ (convert to degrees).
- If the rotation center is not the origin, first find the center (C) by solving for a point equidistant from corresponding vertices, or use vector differences from C to each pair of corresponding points and compute the angle between those vectors.

Send the image or the coordinates and I’ll compute the exact angle and vector.