Question

square cdef is shown on the graph below. cdef is dilated by a scale factor of \\( \frac { 1 } { 2 } \\) centered at \\( ( - 8, - 2 ) \\) to create cdef.

what is the area of cdef?

write your answer as a whole number or as a decimal rounded to the nearest tenth.

square units

Explanation:

Step1: Calculate the side length of square CDEF

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for two - point \((x_1,y_1)\) and \((x_2,y_2)\). Let's take points \(C(-7,-5)\) and \(D(-5,-3)\).

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Step2: Calculate the area of square CDEF

The area of a square \(A = s^2\), where \(s\) is the side length. For square \(CDEF\) with \(s = 2\sqrt{2}\), \(A=(2\sqrt{2})^2=8\).

Step3: Use the property of dilation for area

If a figure is dilated by a scale factor \(k\), the area of the new figure \(A'\) is related to the area of the original figure \(A\) by the formula \(A'=k^{2}A\). Here, \(k = \frac{1}{2}\), so \(A'=(\frac{1}{2})^{2}\times8\).

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Answer:

\(2\)