To find the scale factor of the dilation, we can compare the corresponding side lengths of the original triangle ABC and the dilated triangle A'B'C'.
1. Find the distance between points A and B in triangle ABC.
Using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
AB = √[(-2 - 2)^2 + (2 - 1)^2]
AB = √[(4)^2 + (1)^2]
AB = √[16 + 1]
AB = √17
2. Find the distance between points A' and B' in triangle A'B'C'
Using the distance formula:
A'B' = √[(x2 - x1)^2 + (y2 - y1)^2]
A'B' = √[(-4 - 4)^2 + (4 - 2)^2]
A'B' = √[(-8)^2 + (2)^2]
A'B' = √[64 + 4]
A'B' = √68
A'B' = 2√17
3. The scale factor is the ratio of the corresponding side lengths:
scale factor = A'B' / AB
scale factor = (2√17) / √17
scale factor = 2
Therefore, the scale factor for the dilation of triangle ABC with the center of dilation at the origin (0,0) is 2.
5. 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 the dilation of triangle ABC with a center point of dilation at the origin (0,0).
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