Question

think about the process suppose \\( \triangle p q r \\) 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: Recall the rotation rule

When a point \((x,y)\) is rotated \(270^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(y, - x)\).

Step2: Identify the coordinates of point \(P\)

From the graph, assume the coordinates of point \(P\) are \((1, - 3)\).

Step3: Apply the rotation rule

Using the rule \((x,y)\to(y, - x)\) with \(x = 1\) and \(y=-3\), we get \(P'\) as \((-3,-1)\).

Answer:

\((-3,-1)\)