Question

what is the image point of $(-6,-2)$ after the transformation $d_{\frac{1}{2}}circ r_{270^{circ}}$?

Explanation:

Step1: Apply rotation \(R_{270}\)

The rule for a \(270^{\circ}\) counter - clockwise rotation (\(R_{270}\)) is \((x,y)\to(y, - x)\).
For the point \((-6,-2)\), after rotation: \((-6,-2)\to(-2,6)\)

Step2: Apply dilation \(D_{\frac{1}{2}}\)

The rule for a dilation with scale factor \(k = \frac{1}{2}\) (\(D_{\frac{1}{2}}\)) is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)
For the point \((-2,6)\), after dilation: \((-2,6)\to(\frac{1}{2}\times(-2),\frac{1}{2}\times6)=(-1,3)\)

Answer:

\((-1,3)\)