In the coordinate plane, J'K'L'M' is the image of square JKLM after a dilation with a scale factor of 2.5 centered at (–5,5). The area of JKLM is 48 square units.What is the area of J'K'L'M'?Write your answer as a whole number or decimal. Do not round.
Question
In the coordinate plane, J'K'L'M' is the image of square JKLM after a dilation with a scale factor of 2.5 centered at (–5,5). The area of JKLM is 48 square units.What is the area of J'K'L'M'?Write your answer as a whole number or decimal. Do not round.
Solution
The area of a figure after dilation changes by the square of the scale factor. This is because both the length and the width of the figure are multiplied by the scale factor, and the area of a rectangle (or square) is length times width.
So, if the scale factor of the dilation is 2.5, then the area of the dilated figure (J'K'L'M') will be (2.5)^2 = 6.25 times the area of the original figure (JKLM).
Given that the area of JKLM is 48 square units, the area of J'K'L'M' will be 6.25 * 48 = 300 square units.
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