Triangle FUN, with vertices F(−2, 4), U(0, −5), and N(−3, −8) was dilated to form triangle PET with vertices P(−1.6, 3.2), E(0, −4), and T(−2.4, −6.4).Which scale factor was used?
Looks to me like 0.8
Note that the coordinates are all in the same ratio.
nun of yall gave the answer..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
To determine the scale factor used, we can compare the corresponding side lengths of the two triangles.
Let's calculate the length of side FU for both triangles:
Length of FU in Triangle FUN:
d(F, U) = sqrt((0 - (-2))^2 + (-5 - 4)^2)
= sqrt(2^2 + (-9)^2)
= sqrt(4 + 81)
= sqrt(85)
Length of PE in Triangle PET:
d(P, E) = sqrt((0 - (-1.6))^2 + (-4 - 3.2)^2)
= sqrt(1.6^2 + (-7.2)^2)
= sqrt(2.56 + 51.84)
= sqrt(54.4)
≈ 7.38 (rounded to two decimal places)
Next, let's calculate the length of side UN for both triangles:
Length of UN in Triangle FUN:
d(U, N) = sqrt((-3 - 0)^2 + (-8 - (-5))^2)
= sqrt((-3)^2 + (-3)^2)
= sqrt(9 + 9)
= sqrt(18)
≈ 4.24 (rounded to two decimal places)
Length of ET in Triangle PET:
d(E, T) = sqrt((-2.4 - 0)^2 + (-6.4 - (-4))^2)
= sqrt((-2.4)^2 + (-2.4)^2)
= sqrt(5.76 + 5.76)
= sqrt(11.52)
≈ 3.39 (rounded to two decimal places)
Finally, we can find the scale factor by dividing the corresponding side lengths in the two triangles:
Scale factor = Length of corresponding side in Triangle PET / Length of corresponding side in Triangle FUN
Scale factor for side FU = d(P, E) / d(F, U) ≈ 7.38 / sqrt(85) ≈ 0.83 (rounded to two decimal places)
Scale factor for side UN = d(E, T) / d(U, N) ≈ 3.39 / 4.24 ≈ 0.8 (rounded to two decimal places)
Since the scale factor should be the same for all corresponding sides, we can take the average of the two scale factors:
Average Scale factor = (0.83 + 0.8) / 2 ≈ 0.815 (rounded to three decimal places)
Therefore, the scale factor used to dilate Triangle FUN to form Triangle PET is approximately 0.815.