Question

think about the process suppose (\triangle pqr) is rotated (270^{circ}) about the origin, ((0,0)). find the coordinates of (p^{prime}), (q^{prime}), and (r^{prime}). then sketch (\triangle p^{prime}q^{prime}r^{prime}).
the coordinates of (p^{prime}) are (square). (type an ordered pair)

Explanation:

Step1: Determine the original coordinates of point P

Assume the original coordinates of point \( P \) are \((x,y)\). From the graph (assuming standard grid - based coordinates), if we assume the original point \( P\) has coordinates \((1,-3)\) (by observing the position of the vertex of the triangle on the coordinate grid).

Step2: Apply the rotation formula

The formula for a \(270^{\circ}\) counter - clockwise rotation about the origin \((0,0)\) is \((x,y)\to(y, - x)\).
Substitute \(x = 1\) and \(y=-3\) into the formula:
When \(x = 1\) and \(y=-3\), the new \(x'\) coordinate (of \(P'\)) is \(y=-3\) and the new \(y'\) coordinate (of \(P'\)) is \(-x=-1\).

Answer:

\((-3,1)\)