To determine the type of transformation from triangle ABC to triangle A'B'C', let's evaluate the coordinates of the points provided:
Original triangle (ABC):
- A = (0, 5)
- B = (5, 7)
- C = (7, 0)
Transformed triangle (A'B'C'):
- A' = (0, 2.5)
- B' = (2.5, 3.5)
- C' = (3.5, 0)
We can analyze the transformation by comparing the coordinates of the original triangle with those of the transformed triangle.
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Check Scale Factor:
- The coordinates of A' can be derived from A by multiplying the y-coordinate by a scale factor. Specifically, for A: \[ A' = (0, 5 \times 0.5) = (0, 2.5) \]
- For B: \[ B' = (5 \times 0.5, 7 \times 0.5) = (2.5, 3.5) \]
- For C: \[ C' = (7 \times 0.5, 0 \times 0.5) = (3.5, 0) \]
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Determine the Transformation: From the above calculations, we can see that each point is scaled down by a factor of \(0.5\) in both the x and y coordinates. Therefore, the transformation can be described as a dilation centered at the origin with a scale factor of \(0.5\).
Thus, the transformation that takes triangle ABC to triangle A'B'C' is a dilation with a scale factor of \(0.5\) centered at the origin.