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) Responses
1/2
-2
-1/2
2
To find the scale factor for the dilation of triangle ABC, we need to find the distance between the corresponding points in the original triangle and the dilated triangle.
The distance between points A (-2,4) and A' (-1,2) can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
d = √[(-1 - (-2))^2 + (2 - 4)^2]
= √[(1)^2 + (-2)^2]
= √[1 + 4]
= √5
Similarly, the distance between points B (-6,8) and B' (-3,4) can be found:
d = √[(-3 - (-6))^2 + (4 - 8)^2]
= √[(3)^2 + (-4)^2]
= √[9 + 16]
= √25
= 5
And the distance between points C (-2,4) and C' (-1,2) is also √5.
Since the original distances and the corresponding distances in the dilated triangle are the same, the scale factor of the dilation is 1.
Therefore, the correct answer is: 1.