Transformations and similarity dilations practice
1. Given triangle ABC with vertices A(2,4), B(4,6), and C(6,2). Determine the scale factor for a dilation that would transform triangle ABC to triangle A'B'C' with vertices A'(6,12), B'(12,18), and C'(18,6).
To find the scale factor, we can compare the corresponding side lengths of triangle ABC and triangle A'B'C'.
Side AB:
Distance between A(2,4) and B(4,6) is sqrt((4-2)^2 + (6-4)^2) = sqrt(2^2 + 2^2) = sqrt(8)
Distance between A'(6,12) and B'(12,18) is sqrt((12-6)^2 + (18-12)^2) = sqrt(6^2 + 6^2) = sqrt(72)
Scale factor = sqrt(72) / sqrt(8) = sqrt(9) = 3
Therefore, the scale factor for the dilation is 3.
2. Given triangle DEF with vertices D(-1,0), E(1,2), and F(2,-1). Determine the coordinates of triangle D'E'F' after a dilation with a scale factor of 2.
To find the coordinates of triangle D'E'F', we can multiply the coordinates of triangle DEF by the scale factor.
D' = (-1*2, 0*2) = (-2, 0)
E' = (1*2, 2*2) = (2, 4)
F' = (2*2, -1*2) = (4, -2)
Therefore, triangle D'E'F' has vertices D'(-2,0), E'(2,4), and F'(4,-2) after a dilation with a scale factor of 2.