Question

a rectangle is transformed according to the rule ( r_{0,90^{circ}} ). the image of the rectangle has vertices located at ( p(-4,4) ), ( s(-4,1) ), ( p(-3,1) ), and ( q(-3,4) ). what is the location of ( q )?
( \bigcirc(-4,-3) )
( \bigcirc(-3,-4) )
( \bigcirc(3,4) )
( \bigcirc(4,3) )

Explanation:

Step1: Understand the rotation rule

A rotation of \(180^{\circ}\) about the origin has the rule \((x,y)\to(-x,-y)\).

Step2: Apply the rotation rule to find the pre - image

If the image of a point \(Q'\) is \((- 3,4)\) after a \(180^{\circ}\) rotation about the origin. Let the pre - image of \(Q'\) be \(Q(x,y)\). Using the rule \((x,y)\to(-x,-y)\), we have \(-x=-3\) and \(-y = 4\).

Solving \(-x=-3\) gives \(x = 3\), and solving \(-y=4\) gives \(y=-4\).

Answer:

\((3,-4)\)