Question

write the coordinates of the vertices after a dilation with a scale factor of \frac{1}{2}, centered at the origin.

Explanation:

Step1: Find original coordinates

From the graph, the coordinates are \(S(-8,-10)\), \(T(-8,2)\), \(U(4,2)\), \(V(4,-10)\).

Step2: Apply dilation formula

The formula for dilation centered at the origin is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\).
For \(S(-8,-10)\): \((\frac{1}{2}\times(-8),\frac{1}{2}\times(-10))=(-4,-5)\)
For \(T(-8,2)\): \((\frac{1}{2}\times(-8),\frac{1}{2}\times2)=(-4,1)\)
For \(U(4,2)\): \((\frac{1}{2}\times4,\frac{1}{2}\times2)=(2,1)\)
For \(V(4,-10)\): \((\frac{1}{2}\times4,\frac{1}{2}\times(-10))=(2,-5)\)

Answer:

The coordinates of the vertices after dilation are \(S'(-4,-5)\), \(T'(-4,1)\), \(U'(2,1)\), \(V'(2,-5)\)