Question

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

Explanation:

Step1: Identify the vertices of parallelogram QRST

Assume the vertices of parallelogram QRST are \(Q(x_1,y_1)\), \(R(x_2,y_2)\), \(S(x_3,y_3)\), \(T(x_4,y_4)\). From the graph, if \(Q(- 2,-2)\), \(R(0,-2)\), \(S(2,0)\), \(T(0,0)\).

Step2: Apply the dilation formula

The formula for dilation centered at the origin with scale - factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = 5\).
For point \(Q(-2,-2)\): \((-2\times5,-2\times5)=(-10,-10)\)
For point \(R(0,-2)\): \((0\times5,-2\times5)=(0, - 10)\)
For point \(S(2,0)\): \((2\times5,0\times5)=(10,0)\)
For point \(T(0,0)\): \((0\times5,0\times5)=(0,0)\)

Step3: Graph the new parallelogram

Plot the points \((-10,-10)\), \((0,-10)\), \((10,0)\) and \((0,0)\) on the coordinate - plane and connect them in order to form the dilated parallelogram.

Answer:

Graph the parallelogram with vertices \((-10,-10)\), \((0,-10)\), \((10,0)\) and \((0,0)\) on the given coordinate - grid.