Question

think about the process suppose \\( \triangle p q r \\) is rotated \\( 90^{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 \\( (-2,3) \\). (type an ordered pair.)
the coordinates of \\( q^{prime} \\) are \\( \square \\). (type an ordered pair.)

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by \((-y,x)\).

Step2: Find the coordinates of \(Q\)

From the graph, the coordinates of \(Q\) are \((4,2)\).

Step3: Apply the rotation rule to \(Q\)

Using the rule \((x,y)\to(-y,x)\), for \(x = 4\) and \(y=2\), we have \(x'=-2\) and \(y' = 4\).

Answer:

The coordinates of \(Q'\) are \((- 2,4)\)