Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{2}$, centered at the origin.
$r(\\ ,\\ )$
$s(\\ ,\\ )$
$t(\\ ,\\ )$

Explanation:

Step1: Find the original coordinates

From the graph, we can see that \(R(-4,-6)\), \(S(8,-6)\), \(T(8,-2)\), \(U(-4,-2)\)

Step2: Apply the dilation formula

The formula for dilation centered at the origin is \((x,y)\to(kx,ky)\), where \(k = \frac{1}{2}\)
For point \(R(-4,-6)\):
\(x=-4\times\frac{1}{2}=-2\), \(y = -6\times\frac{1}{2}=-3\)
For point \(S(8,-6)\):
\(x=8\times\frac{1}{2}=4\), \(y=-6\times\frac{1}{2}=-3\)
For point \(T(8,-2)\):
\(x=8\times\frac{1}{2}=4\), \(y=-2\times\frac{1}{2}=-1\)
For point \(U(-4,-2)\):
\(x=-4\times\frac{1}{2}=-2\), \(y=-2\times\frac{1}{2}=-1\)

Answer:

\(R(-2,-3)\), \(S(4,-3)\), \(T(4,-1)\), \(U(-2,-1)\)