Question

1. graph the image of the trapezoid below using a scale factor of $k = 3/2$.

Explanation:

Step1: Determine the coordinates of original points

Assume the coordinates of \(R\) is \((- 6,1)\), \(S\) is \((-2,2)\), \(T\) is \((-2,-3)\), \(U\) is \((-6,-3)\)

Step2: Use the scale - factor formula for dilation

If the scale factor is \(k=\frac{3}{2}\) and the formula for dilation is \((x,y)\to(kx,ky)\)

• For point \(R(-6,1)\):

\(x'=\frac{3}{2}\times(-6)=-9\), \(y'=\frac{3}{2}\times1 = 1.5\)

• For point \(S(-2,2)\):

\(x'=\frac{3}{2}\times(-2)=-3\), \(y'=\frac{3}{2}\times2=3\)

• For point \(T(-2,-3)\):

\(x'=\frac{3}{2}\times(-2)=-3\), \(y'=\frac{3}{2}\times(-3)=-4.5\)

• For point \(U(-6,-3)\):

\(x'=\frac{3}{2}\times(-6)=-9\), \(y'=\frac{3}{2}\times(-3)=-4.5\)

Answer:

\(R'(-9,1.5)\), \(S'(-3,3)\), \(T'(-3,-4.5)\), \(U'(-9,-4.5)\)