Question

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

Explanation:

Step1: Find original coordinates

From the graph, \(C(-2,-2)\), \(D(2,-2)\), \(E(2,0)\), \(F(-2,0)\)

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 \(C(-2,-2)\): \((-2\times5,-2\times5)=(-10,-10)\)
• For \(D(2,-2)\): \((2\times5,-2\times5)=(10,-10)\)
• For \(E(2,0)\): \((2\times5,0\times5)=(10,0)\)
• For \(F(-2,0)\): \((-2\times5,0\times5)=(-10,0)\)

Answer:

\(C'(-10,-10)\), \(D'(10,-10)\), \(E'(10,0)\), \(F'(-10,0)\)