Question
triangle on coordinate plane was dilated, after dilation its area is 6.25 times as great as the original figure. what is the scale factor
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Answered by
GPT-4o mini
The area of a shape that has been dilated by a scale factor \( k \) changes by a factor of \( k^2 \). This means that if the area of the dilated triangle is 6.25 times the area of the original triangle, we can set up the equation:
\[
k^2 = 6.25
\]
To find the scale factor \( k \), we take the square root of both sides:
\[
k = \sqrt{6.25}
\]
Calculating the square root:
\[
k = 2.5
\]
Thus, the scale factor for the dilation is \( 2.5 \).
\[
k^2 = 6.25
\]
To find the scale factor \( k \), we take the square root of both sides:
\[
k = \sqrt{6.25}
\]
Calculating the square root:
\[
k = 2.5
\]
Thus, the scale factor for the dilation is \( 2.5 \).
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