Question 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) . (1 point)
To find the scale factor for the dilation, we can compare the distances between the corresponding points of each triangle.
First, let's calculate the distance between points A and B of triangle ABC:
AB = √[(-6 - (-2))^2 + (8 - 4)^2] = √[16 + 16] = √32 = 4√2
Now, let's calculate the distance between points A' and B' of triangle A'B'C':
A'B' = √[(-3 - (-1))^2 + (4 - 2)^2] = √[4 + 4] = 2√2
The scale factor can be found by dividing the distance of A'B' by the distance of AB:
Scale factor = A'B' / AB = (2√2) / (4√2) = 1/2
Therefore, the scale factor for the dilation of triangle ABC is 1/2.