Question

Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one eighth to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′. A′(3.5, −5.25), B′(1.75, −1.75), C′(−3.5, 1.75), D′(−3.5, −3.5) A′(3.2, −4.8), B′(1.6, −1.6), C′(−3.2, 1.6), D′(3.2, 3.2) A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5) A′(−12, 14), B′(−10, 10), C′(12, −14), D′(12, 12)

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given vertices of the polygon

`\begin{gathered} A(-4,6) \\ B(-2,2) \\ C(4,-2) \\ D(4,4) \end{gathered}`

STEP 2: Write the given scale factor

`scale-factor=(1)/(8)`

STEP 3: Find the vertices of the new polygon A′B′C′D′

To get the new vertices, we multiply the old vertices by the given scale factor, therefore,

`\begin{gathered} A^(\prime)=((1)/(8)*-4,(1)/(8)*6)=(-0.5,0.75) \\ \\ B^(\prime)=((1)/(8)*-2,(1)/(8)*2)=(-(2)/(8),(2)/(8))=(-0.25,0.25) \\ \\ C^(\prime)=((1)/(8)*4,(1)/(8)*-2)=(0.5,-0.25) \\ \\ D^(\prime)=((1)/(8)*4,(1)/(8)*4)=(0.5,0.5) \end{gathered}`

Hence, the vertices of polygon A′B′C′D′ are given as:

`A^(\prime)\left(−0.5,\:0.75\right),\:B^(\prime)\left(−0.25,\:0.25\right),\:C^(\prime)\left(0.5,\:−0.25\right),\:D^(\prime)\left(0.5,\:0.5\right)`