Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if a point has coordinates \((x,y)\), its new coordinates \((x',y')\) after dilation are given by \((x',y')=(kx,ky)\), where \(k = 4\) in this case.

Step2: Find coordinates of point \(P\)

The coordinates of point \(P\) are \((- 2,-1)\). Using the dilation formula, \(x'=4\times(-2)=-8\) and \(y'=4\times(-1)=-4\). So the new coordinates of \(P\) are \((-8,-4)\).

Step3: Find coordinates of point \(Q\)

The coordinates of point \(Q\) are \((-2,2)\). Then \(x'=4\times(-2)=-8\) and \(y'=4\times2 = 8\). So the new coordinates of \(Q\) are \((-8,8)\).

Step4: Find coordinates of point \(R\)

The coordinates of point \(R\) are \((2,2)\). So \(x'=4\times2=8\) and \(y'=4\times2 = 8\). The new coordinates of \(R\) are \((8,8)\).

Step5: Find coordinates of point \(S\)

The coordinates of point \(S\) are \((2,-1)\). Then \(x'=4\times2=8\) and \(y'=4\times(-1)=-4\). So the new coordinates of \(S\) are \((8,-4)\).

Answer:

\(P(-8,-4)\), \(Q(-8,8)\), \(R(8,8)\), \(S(8,-4)\)