Question

graph the image of parallelogram stuv after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify the coordinates of the parallelogram vertices

From the graph, assume \(S(-3,-2)\), \(T(-1,-2)\), \(U(1,1)\), \(V(-1,1)\)

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor \(k = 4\), the formula for the image of a point \((x,y)\) is \((kx,ky)\).
For point \(S(-3,-2)\): \((4\times(-3),4\times(-2))=(-12,-8)\)
For point \(T(-1,-2)\): \((4\times(-1),4\times(-2))=(-4,-8)\)
For point \(U(1,1)\): \((4\times1,4\times1)=(4,4)\)
For point \(V(-1,1)\): \((4\times(-1),4\times1)=(-4,4)\)

Step3: Graph the new parallelogram

Plot the points \((-12,-8)\), \((-4,-8)\), \((4,4)\), \((-4,4)\) and connect them in order to form the dilated parallelogram.

Answer:

Graph the parallelogram with vertices \((-12,-8)\), \((-4,-8)\), \((4,4)\), \((-4,4)\) on the given coordinate - plane.