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 \(k = 5\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \((x',y')=(k\times x,k\times y)\)
For point \(U(-1,-2)\):
\(x'=5\times(-1)=-5\), \(y'=5\times(-2)=-10\), so \(U'(-5,-10)\)
For point \(V(-1,2)\):
\(x'=5\times(-1)=-5\), \(y'=5\times2 = 10\), so \(V'(-5,10)\)
For point \(W(1,-2)\):
\(x'=5\times1 = 5\), \(y'=5\times(-2)=-10\), so \(W'(5,-10)\)

Answer:

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