Question

Which of the following describes the rotation shown? triangles s t u and s prime t prime u prime on a coordinate plane. triangle s t u has coordinates s negative 4 comma 2, t negative 1 comma 3, and u negative 2 comma 1. triangle s prime t prime u prime has coordinates s prime 4 comma negative 2, t prime 1 comma negative 3, and u prime 2 comma negative 1. Δs't'u' is a _______ rotation about the origin of Δstu.

1) 90°
2) 180°
3) 270°
4) 360°

Answer 1

ΔS'T'U' is a 180° rotation about the origin of ΔSTU. This conclusion is drawn from analyzing the change in the signs of the coordinates from S to S', T to T', and U to U'.

Step-by-step explanation:

The student is asking about a geometric transformation of a triangle on a coordinate plane, specifically a rotation about the origin. When ΔSTU with coordinates S(-4, 2), T(-1, 3), and U(-2, 1) is transformed to ΔS'T'U' with coordinates S'(4, -2), T'(1, -3), and U'(2, -1), we need to determine the angle of rotation around the origin.

To identify the correct rotation, we compare the coordinates pre- and post-rotation. For instance, looking at point S moving to S', we see that the x-coordinate has changed from -4 to 4 and the y-coordinate from 2 to -2. This indicates that points have been rotated 180° around the origin because the sign of both the x-coordinate and y-coordinate has been inverted, which is characteristic of a 180° rotation.

Thus, we can conclude that ΔS'T'U' is a 180° rotation about the origin of ΔSTU.