Question

dilate the trapezoid using center (0,0) and scale factor 2.

Explanation:

Step1: Identify original coordinates

Let \(A(-3,-2)\), \(B(1,-2)\), \(C(0,1)\), \(D(-2,1)\)

Step2: Apply dilation formula

For a dilation with center \((0,0)\) and scale - factor \(k = 2\), the formula for a point \((x,y)\) is \((x',y')=(k\cdot x,k\cdot y)\)
For point \(A(-3,-2)\): \(A'=(2\times(-3),2\times(-2))=(-6,-4)\)
For point \(B(1,-2)\): \(B'=(2\times1,2\times(-2))=(2,-4)\)
For point \(C(0,1)\): \(C'=(2\times0,2\times1)=(0,2)\)
For point \(D(-2,1)\): \(D'=(2\times(-2),2\times1)=(-4,2)\)

Answer:

The new coordinates of the dilated trapezoid are \(A'(-6,-4)\), \(B'(2,-4)\), \(C'(0,2)\), \(D'(-4,2)\)