Question

point q was rotated 180° about the origin. the resulting point q was translated up 5 units to the point q(-4,3).
give the coordinates of point q:

Explanation:

Step1: Reverse the translation

Translation up \(5\) units is \( (x,y)\to(x,y + 5)\). To reverse it, we use \( (x,y)\to(x,y-5)\).
For point \(Q''(-4,3)\), reversing the translation: \(Q'(-4,3 - 5)=(-4,-2)\)

Step2: Reverse the rotation

Rotation of \(180^{\circ}\) about the origin is \( (x,y)\to(-x,-y)\). To reverse it, we use \( (x,y)\to(-x,-y)\) again.
For point \(Q'(-4,-2)\), reversing the rotation: \(Q=-(-4),-(-2)=(4,2)\)

Answer:

\((4,2)\)