Question

graph the image of rectangle efgh after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify the original coordinates

Let \(E(-3,2)\), \(F(1,2)\), \(G(1,3)\), \(H(-3,3)\)

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor \(k = 3\), the formula for a point \((x,y)\) is \((x',y')=(k\cdot x,k\cdot y)\)
For point \(E\): \(E'=(3\times(-3),3\times2)=(-9,6)\)
For point \(F\): \(F'=(3\times1,3\times2)=(3,6)\)
For point \(G\): \(G'=(3\times1,3\times3)=(3,9)\)
For point \(H\): \(H'=(3\times(-3),3\times3)=(-9,9)\)

Step3: Graph the new rectangle

Plot the points \(E'(-9,6)\), \(F'(3,6)\), \(G'(3,9)\), \(H'(-9,9)\) and connect them to form the dilated rectangle.

Answer:

The new rectangle has vertices \(E'(-9,6)\), \(F'(3,6)\), \(G'(3,9)\), \(H'(-9,9)\)