Question
If ΔABC is dilated by a scale factor of 1/2
with a dilation center at vertex A, by what factor does the area of the triangle decrease?
with a dilation center at vertex A, by what factor does the area of the triangle decrease?
Answers
GPT-4o mini
When a triangle is dilated by a scale factor, the area of the triangle changes by the square of the scale factor.
In this case, the scale factor for the dilation is \( \frac{1}{2} \). To find the factor by which the area decreases, we need to square the scale factor:
\[
\text{Area factor} = \left(\frac{1}{2}\right)^2 = \frac{1}{4}
\]
This means that the area of triangle \( \Delta ABC \) after dilation will be \( \frac{1}{4} \) of the original area.
Therefore, the area of the triangle decreases by a factor of \( \frac{1}{4} \), or in other words, the new area is 1/4 of the original area. The original area decreases to 1/4, indicating a reduction in area by 75%.
In this case, the scale factor for the dilation is \( \frac{1}{2} \). To find the factor by which the area decreases, we need to square the scale factor:
\[
\text{Area factor} = \left(\frac{1}{2}\right)^2 = \frac{1}{4}
\]
This means that the area of triangle \( \Delta ABC \) after dilation will be \( \frac{1}{4} \) of the original area.
Therefore, the area of the triangle decreases by a factor of \( \frac{1}{4} \), or in other words, the new area is 1/4 of the original area. The original area decreases to 1/4, indicating a reduction in area by 75%.