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 of the vertices are: D(-3,-2), E(0,-2), F(0, - 2), G(-3,-2).

Step2: Apply dilation formula

For a dilation with scale factor \(k = 5\) centered at the origin \((x,y)\to(kx,ky)\).
For point D(-3,-2): \(x=-3,y = - 2\), new - coordinates are \(D'=(5\times(-3),5\times(-2))=(-15,-10)\)
For point E(0,-2): \(x = 0,y=-2\), new - coordinates are \(E'=(5\times0,5\times(-2))=(0,-10)\)
For point F(1,-2): \(x = 1,y=-2\), new - coordinates are \(F'=(5\times1,5\times(-2))=(5,-10)\)
For point G(-3,-2): \(x=-3,y = - 2\), new - coordinates are \(G'=(5\times(-3),5\times(-2))=(-15,-10)\)

Answer:

D'(-15,-10), E'(0,-10), F'(5,-10), G'(-15,-10)