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 dilation of triangle abc with a center point of dilation at the origin 0,0
To find the scale factor for the dilation, you can compare the corresponding side lengths of the two triangles.
Let's start with side AB.
The length of side AB in triangle ABC is given by the distance formula:
d(AB) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-2 - 2)^2 + (2 - 1)^2)
= sqrt(16 + 1)
= sqrt(17)
The length of side A'B' in triangle A'B'C' is given by the distance formula:
d(A'B') = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-4 - 4)^2 + (4 - 2)^2)
= sqrt(64 + 4)
= sqrt(68)
= 2 sqrt(17)
So, the scale factor for side AB is:
scale factor AB = d(A'B') / d(AB)
= (2 sqrt(17)) / sqrt(17)
= 2
Repeating the same steps for the other sides will give you the scale factor for the entire triangle. In this case, since the dilation is centered at the origin (0,0), all sides will have the same scale factor of 2.