Question

1. graph the image of the trapezoid below using a scale factor of $k = 1/4$

Explanation:

Step1: Recall the rule for dilation

When a point \((x,y)\) is dilated with a scale factor \(k\), the new point \((x',y')\) is given by \((x',y')=(k\times x,k\times y)\)

Step2: Find \(F'\)

For point \(F(2,8)\) and \(k = \frac{1}{4}\), we have \(x'=\frac{1}{4}\times2=\frac{1}{2}\) and \(y'=\frac{1}{4}\times8 = 2\). So \(F'(\frac{1}{2},2)\)

Step3: Find \(G'\)

For point \(G(4,8)\) and \(k=\frac{1}{4}\), \(x'=\frac{1}{4}\times4 = 1\) and \(y'=\frac{1}{4}\times8=2\). So \(G'(1,2)\)

Step4: Find \(H'\)

For point \(H(8,4)\) and \(k=\frac{1}{4}\), \(x'=\frac{1}{4}\times8 = 2\) and \(y'=\frac{1}{4}\times4=1\). So \(H'(2,1)\)

Step5: Find \(I'\)

For point \(I(- 4,-4)\) and \(k=\frac{1}{4}\), \(x'=\frac{1}{4}\times(-4)=-1\) and \(y'=\frac{1}{4}\times(-4)=-1\). So \(I'(-1,-1)\)

Answer:

\(F'(\frac{1}{2},2)\), \(G'(1,2)\), \(H'(2,1)\), \(I'(-1,-1)\)