To find the scale factor of the dilation, we can compare the side lengths of the original triangle ABC and the dilated triangle A'B'C'.
Using the distance formula, we can calculate the side lengths of triangle ABC:
AB = sqrt((-6 - (-2))^2 + (8 - 4)^2) = sqrt((-4)^2 + 4^2) = sqrt(16 + 16) = sqrt(32) = 4√2
BC = sqrt((-2 - (-6))^2 + (4 - 8)^2) = sqrt(4^2 + (-4)^2) = sqrt(16 + 16) = sqrt(32) = 4√2
AC = sqrt((-6 - (-2))^2 + (8 - 4)^2) = sqrt((-4)^2 + 4^2) = sqrt(16 + 16) = sqrt(32) = 4√2
Next, we can calculate the side lengths of triangle A'B'C':
A'B' = sqrt((-3 - (-1))^2 + (4 - 2)^2) = sqrt((-2)^2 + 2^2) = sqrt(4 + 4) = sqrt(8) = 2√2
B'C' = sqrt((-1 - (-3))^2 + (2 - 4)^2) = sqrt(2^2 + (-2)^2) = sqrt(4 + 4) = sqrt(8) = 2√2
A'C' = sqrt((-3 - (-1))^2 + (4 - 2)^2) = sqrt((-2)^2 + 2^2) = sqrt(4 + 4) = sqrt(8) = 2√2
Finally, we can find the scale factor by comparing the side lengths:
Scale factor = A'B' / AB = (2√2) / (4√2) = 2√2 / 4√2 = (2/4) * (√2/√2) = 1/2
Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 1/2.
triangle abc has vertices point a -2 4 point b -6, 8 and point c -2, 4 after dilation triangle a'b'c' has vertices point a' -1, 2 point b' -3 4 and point c' -1, 2 determine the scale factor for the dilation of triangle abc with a center point of dilation at the origin 0,0
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since the center of dilation is (0,0) just note that all of the coordinates have been multiplied by 1/2. That is the scale factor.
You are correct. Since the center of dilation is at the origin (0,0) and all the coordinates have been multiplied by 1/2, the scale factor for the dilation of triangle ABC is 1/2.
1 answer