Question

trapezoid lmno is shown on the graph below. lmno is dilated by a scale factor of 3 centered at the origin to create lmno. what is the area of lmno? write your answer as a whole number or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Find the coordinates of the original trapezoid

From the graph, \(L(-8,8)\), \(M(-4,2)\), \(N(-4,-6)\), \(O(-8,-8)\). The formula for the area of a trapezoid is \(A=\frac{1}{2}(b_1 + b_2)h\). Here, \(b_1\) (the length of the top - base) is the distance between \(L\) and \(M\) in the \(y\) - direction. \(b_1=8 - 2=6\). \(b_2\) (the length of the bottom - base) is the distance between \(O\) and \(N\) in the \(y\) - direction. \(b_2=\vert-8-(-6)\vert = 2\). The height \(h\) is the distance between \(x=-8\) and \(x = - 4\), so \(h=\vert-4-(-8)\vert=4\).

Step2: Calculate the area of the original trapezoid

Using the trapezoid area formula \(A=\frac{1}{2}(b_1 + b_2)h\), substitute \(b_1 = 6\), \(b_2=2\), and \(h = 4\).

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Step3: Use the property of dilation for area

When 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, \(k = 3\).

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Answer:

\(144\)