Triangle ABC had vertices point A(-2,4), point B(-6,8), and point C(-2,4). After dilation, triangle A’B’C’ had vertices point A’(-1,2), point B’(-3,4), and poor C’(-1,2). Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0,0).

Answer 1

To find the scale factor for the dilation, we can compare the corresponding distances between the corresponding vertices of the two triangles.

The distance between points A(-2, 4) and B(-6, 8) is determined using the distance formula:

d(A, B) = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d(A, B) = sqrt((-6 - (-2))^2 + (8 - 4)^2) = sqrt((-4)^2 + 4^2) = sqrt(16 + 16) = sqrt(32) = 4*sqrt(2)

The distance between points A'(-1, 2) and B'(-3, 4) is:

d(A', B') = sqrt((-3 - (-1))^2 + (4 - 2)^2) = sqrt((-2)^2 + 2^2) = sqrt(4 + 4) = sqrt(8) = 2*sqrt(2)

Therefore, the scale factor for the dilation is:

d(A', B') / d(A, B) = (2*sqrt(2)) / (4*sqrt(2)) = 2 / 4 = 1/2

Hence, the scale factor for the dilation of triangle ABC is 1/2.