A triangle on a coordinate plane was dilated. After being dilated, its area is 6.25 times as great as the original figure. What was the scale factor?(1 point)
Let's assume the original triangle has an area of A, and the dilated triangle has an area of B.
Since the area of the dilated triangle is 6.25 times as great as the original figure, we can write:
B = 6.25A
We know that the scale factor, denoted as k, is the ratio of corresponding side lengths.
Since the area of a triangle is proportional to the square of its side lengths, we can write:
B = k^2 * A
Since we have the equation B = 6.25A from earlier, we can substitute it into the equation above:
6.25A = k^2 * A
We can cancel out the A's on both sides:
6.25 = k^2
To solve for k, we need to find the square root of both sides:
√(6.25) = √(k^2)
Taking the square root of both sides:
k = √(6.25) = 2.5
Therefore, the scale factor is 2.5.