Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
one half
3
one third
The scale factor used in this dilation is 2.
This can be determined by comparing the distance between any two corresponding points in the two triangles. For example, the distance between points A and A' is sqrt(((-1)-(-3))^2 + ((-1) - (-3))^2) = sqrt(2^2 + 2^2) = sqrt(8), while the distance between points B and B' is sqrt((1-3)^2 + (1-3)^2) = sqrt(8). Since these distances are equal, the scale factor is 2.