Question

write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates are \(U(-1,- 2)\), \(V(-1,2)\), \(W(1,-2)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k\), the formula is \((x,y)\to(kx,ky)\). Here \(k = 5\).
For point \(U(-1,-2)\): \(U'=(5\times(-1),5\times(-2))=(-5,-10)\).
For point \(V(-1,2)\): \(V'=(5\times(-1),5\times2)=(-5,10)\).
For point \(W(1,-2)\): \(W'=(5\times1,5\times(-2))=(5,-10)\).

Answer:

\(U'(-5,-10)\)
\(V'(-5,10)\)
\(W'(5,-10)\)