To find the scale factor, we can compare the corresponding side lengths of the original triangle ABC and the dilated triangle A'B'C'.
Let's find the length of side AB in both triangles:
Length of AB in triangle ABC:
AB = sqrt((x2-x1)^2 + (y2-y1)^2)
AB = sqrt((-2-2)^2 + (2-1)^2)
AB = sqrt((-4)^2 + (1)^2)
AB = sqrt(16 + 1)
AB = sqrt(17)
Length of A'B' in triangle A'B'C':
A'B' = sqrt((x2-x1)^2 + (y2-y1)^2)
A'B' = sqrt((-4-4)^2 + (4-2)^2)
A'B' = sqrt((-8)^2 + (2)^2)
A'B' = sqrt(64 + 4)
A'B' = sqrt(68)
A'B' = 2sqrt(17)
The scale factor is the ratio of the corresponding side lengths: A'B' / AB
Scale factor = 2sqrt(17) / sqrt(17)
Scale factor = 2
Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 2.
Triangle ABC has vertices point A(2, 1) , point B(−2, 2) , and point C(−3,−1) . After dilation, triangle A′B′C′ has vertices point A′(4, 2) , point B′(−4, 4) , and point C′(−6,−2) . Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0, 0 ) .(1 point)
1 answer