Questions: The rectangle E'F'GH' is a dilation of the rectangle EFGH. What is the scale factor of the dilation? Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

The rectangle E'F'GH' is a dilation of the rectangle EFGH. What is the scale factor of the dilation? Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
Transcript text: The rectangle E'F'GH' is a dilation of the rectangle EFGH. What is the scale factor of the dilation? Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
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Solution

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Solution Steps

Step 1: Find the coordinates of the vertices of rectangle EFGH.

The coordinates of the vertices of rectangle EFGH are: E(-3, 3) F(2, 3) G(2, -3) H(-3, -3)

Step 2: Find the coordinates of the vertices of rectangle E'F'G'H'.

The coordinates of the vertices of rectangle E'F'G'H' are: E'(-9, 9) F'(6, 9) G'(6, -9) H'(-9, -9)

Step 3: Calculate the lengths of the sides of both rectangles.

Length of EF = 2 - (-3) = 5 Length of FG = 3 - (-3) = 6 Length of GH = -3 - (-3) = 5 Length of HE = -3 - 2 = 6

Length of E'F' = 6 - (-9) = 15 Length of F'G' = 9 - (-9) = 18 Length of G'H' = 6 - (-9) = 15 Length of H'E' = -9 - (-9) = 18

Step 4: Calculate the scale factor.

The scale factor is the ratio of the corresponding side lengths of the dilated rectangle to the original rectangle.

Scale factor = E'F'/EF = 15/5 = 3 Scale factor = F'G'/FG = 18/6 = 3 Scale factor = G'H'/GH = 15/5 = 3 Scale factor = H'E'/HE = 18/6 = 3

Final Answer:

The scale factor of the dilation is \(\boxed{3}\).

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