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 in the original triangle and the dilated triangle.
For example, let's compare the distance between point A (-2, 4) and the origin (0, 0) in the original triangle to the distance between point A' (-1, 2) and the origin (0, 0) in the dilated triangle.
Distance between point A and the origin in the original triangle:
√((-2-0)^2 + (4-0)^2) = √(4 + 16) = √20
Distance between point A' and the origin in the dilated triangle:
√((-1-0)^2 + (2-0)^2) = √(1 + 4) = √5
The scale factor can be calculated as the ratio of these distances:
Scale factor = Distance in dilated triangle / Distance in original triangle = √5 / √20
To simplify this ratio, we can rationalize the denominator:
Scale factor = (√5 / √20) * (√20 / √20) = (√100) / (√400) = 10 / 20 = 1/2
Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 1/2.