Question

graph the image of rectangle defg after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Identify rectangle vertices

Assume \(D(-1,-2)\), \(E(1,-2)\), \(F(1,2)\), \(G(-1,2)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 5\), the formula is \((x,y)\to(kx,ky)\).
For point \(D(-1,-2)\), the new point \(D'=5\times(-1),5\times(-2)=(-5,-10)\)
For point \(E(1,-2)\), the new point \(E'=5\times1,5\times(-2)=(5,-10)\)
For point \(F(1,2)\), the new point \(F'=5\times1,5\times2=(5,10)\)
For point \(G(-1,2)\), the new point \(G'=5\times(-1),5\times2=(-5,10)\)

Step3: Graph new rectangle

Plot the points \(D'(-5,-10)\), \(E'(5,-10)\), \(F'(5,10)\), \(G'(-5,10)\) and connect them to form the dilated rectangle.

Answer:

Graph the rectangle with vertices \(D'(-5,-10)\), \(E'(5,-10)\), \(F'(5,10)\), \(G'(-5,10)\)