Question

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

Explanation:

Step1: Identify the original vertices

Assume the coordinates of the vertices of trapezoid \(PQRS\) are \(P(x_1,y_1)\), \(Q(x_2,y_2)\), \(R(x_3,y_3)\), \(S(x_4,y_4)\). From the graph, if we assume \(P(1, - 2)\), \(Q(2,-2)\), \(R(2,1)\), \(S(-1,1)\).

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor \(k = 4\), the formula for the coordinates of the dilated point \((x',y')\) of a point \((x,y)\) is \(x'=k\times x\) and \(y'=k\times y\).
For point \(P(1,-2)\): \(P'(4\times1,4\times(-2))=(4,-8)\)
For point \(Q(2,-2)\): \(Q'(4\times2,4\times(-2))=(8,-8)\)
For point \(R(2,1)\): \(R'(4\times2,4\times1)=(8,4)\)
For point \(S(-1,1)\): \(S'(4\times(-1),4\times1)=(-4,4)\)

Step3: Graph the new trapezoid

Plot the points \(P'(4,-8)\), \(Q'(8,-8)\), \(R'(8,4)\), \(S'(-4,4)\) on the coordinate - plane and connect them in order to get the dilated trapezoid.

Answer:

Graph the trapezoid with vertices \((4,-8)\), \((8,-8)\), \((8,4)\), \((-4,4)\) on the given coordinate - grid.