Question

graph the image of parallelogram bcde after a dilation with a scale factor of $\frac{1}{5}$, centered at the origin.

Explanation:

Step1: Find the coordinates of the original parallelogram

From the graph, we can see that \(B(0,-10)\), \(C(0,5)\), \(D(10,10)\), \(E(10,-5)\)

Step2: Apply the dilation formula

The dilation formula centered at the origin is \((x,y)\to(\frac{1}{5}x,\frac{1}{5}y)\)

• For point \(B(0,-10)\): \((\frac{1}{5}\times0,\frac{1}{5}\times(-10))=(0, - 2)\)
• For point \(C(0,5)\): \((\frac{1}{5}\times0,\frac{1}{5}\times5)=(0,1)\)
• For point \(D(10,10)\): \((\frac{1}{5}\times10,\frac{1}{5}\times10)=(2,2)\)
• For point \(E(10,-5)\): \((\frac{1}{5}\times10,\frac{1}{5}\times(-5))=(2,-1)\)

Step3: Plot the new points

Plot the points \(B'(0,-2)\), \(C'(0,1)\), \(D'(2,2)\), \(E'(2,-1)\) and connect them to form the dilated parallelogram.

Answer:

The coordinates of the image of parallelogram \(BCDE\) after dilation are \(B'(0,-2)\), \(C'(0,1)\), \(D'(2,2)\), \(E'(2,-1)\)