Question

test prep what rotation of △mnp about point p could have produced △pqr (image of grid with points m, n, p, q, r) show hints 180° clockwise 90° clockwise 270° counterclockwise 360° counterclockwise

Explanation:

Step1: Analyze rotation properties

A \(180^\circ\) rotation about a point \(P\) maps a point \((x,y)\) to \((-x + 2p_x, -y + 2p_y)\) (where \(p_x,p_y\) are coordinates of \(P\)). Visually, for \(\triangle MNP\) and \(\triangle PQR\), the relative positions suggest a \(180^\circ\) rotation: segments from \(P\) to corresponding vertices are reversed in direction.

Step2: Eliminate other options

• \(90^\circ\) clockwise would rotate vertices to a perpendicular direction, not matching the figure.
• \(270^\circ\) counterclockwise is equivalent to \(90^\circ\) clockwise, also not matching.
• \(360^\circ\) rotation leaves the figure unchanged, which is not the case here.

Answer:

\(180^\circ\) clockwise