contestada

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)

Respuesta :

SOLUTION

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

[tex]\begin{gathered} A(-4,6) \\ B(-2,2) \\ C(4,-2) \\ D(4,4) \end{gathered}[/tex]

STEP 2: Write the given scale factor

[tex]scale-factor=\frac{1}{8}[/tex]

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,

[tex]\begin{gathered} A^{\prime}=(\frac{1}{8}\times-4,\frac{1}{8}\times6)=(-0.5,0.75) \\ \\ B^{\prime}=(\frac{1}{8}\times-2,\frac{1}{8}\times2)=(-\frac{2}{8},\frac{2}{8})=(-0.25,0.25) \\ \\ C^{\prime}=(\frac{1}{8}\times4,\frac{1}{8}\times-2)=(0.5,-0.25) \\ \\ D^{\prime}=(\frac{1}{8}\times4,\frac{1}{8}\times4)=(0.5,0.5) \end{gathered}[/tex]

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

[tex]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)[/tex]

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