Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{5}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

Assume \(B(- 10,0)\), \(C(-10,5)\), \(D(10,5)\), \(E(10,0)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = \frac{1}{5}\), if the original point is \((x,y)\), the new point \((x',y')=(k x,k y)\).
For point \(B(-10,0)\): \(x'=\frac{1}{5}\times(-10)= - 2\), \(y'=\frac{1}{5}\times0 = 0\), new \(B'(-2,0)\)
For point \(C(-10,5)\): \(x'=\frac{1}{5}\times(-10)=-2\), \(y'=\frac{1}{5}\times5 = 1\), new \(C'(-2,1)\)
For point \(D(10,5)\): \(x'=\frac{1}{5}\times10 = 2\), \(y'=\frac{1}{5}\times5=1\), new \(D'(2,1)\)
For point \(E(10,0)\): \(x'=\frac{1}{5}\times10 = 2\), \(y'=\frac{1}{5}\times0 = 0\), new \(E'(2,0)\)

Answer:

\(B'(-2,0)\), \(C'(-2,1)\), \(D'(2,1)\), \(E'(2,0)\)