Question

1
what degree of rotation about the origin will cause the triangle below to map onto itself?

a. 270°
b. 180°
c. 90°
d. 360°

Explanation:

Step1: Recall Rotation Properties

A rotation of \(360^\circ\) about any point (including the origin) maps a figure onto itself, as it's a full rotation back to the original position. For other rotations (\(90^\circ\), \(180^\circ\), \(270^\circ\)), we check symmetry. The triangle is isoceles but not symmetric for \(90^\circ\), \(180^\circ\), or \(270^\circ\) rotations (since it's not centered at the origin in a way that those rotations would map it to itself, but a \(360^\circ\) rotation always works).

Step2: Evaluate Each Option

• \(90^\circ\): Rotating the triangle \(90^\circ\) (clockwise or counterclockwise) about the origin will move it to a new position, not overlapping with the original.
• \(180^\circ\): Rotating \(180^\circ\) will flip the triangle across the origin, but its position (due to coordinates) won't match the original.
• \(270^\circ\): Similar to \(90^\circ\), the triangle won't map to itself.
• \(360^\circ\): A full rotation, so the triangle returns to its original position.

Answer:

D. \(360^\circ\)