To determine the transformation that maps triangle ABC to triangle A'B'C', we should first examine the coordinates of both triangles.
For triangle ABC:
- Point A: (0, 5)
- Point B: (5, 7)
- Point C: (7, 0)
For triangle A'B'C':
- Point A': (0, 2.5)
- Point B': (2.5, 3.5)
- Point C': (3.5, 0)
Next, we can observe the coordinates of each corresponding point:
- Point A to A': From (0, 5) to (0, 2.5) - this is a vertical shrink by a factor of 0.5 (y-coordinate halves).
- Point B to B': From (5, 7) to (2.5, 3.5) - we can see that both the x-coordinate and y-coordinate are halved. The x-coordinate goes from 5 to 2.5, and the y-coordinate goes from 7 to 3.5, which is also shrunk by a factor of 0.5.
- Point C to C': From (7, 0) to (3.5, 0) - again, the x-coordinate is halved (from 7 to 3.5) while the y-coordinate remains the same.
Since all corresponding points in triangle ABC are reduced in size to half their original dimensions in triangle A'B'C', the transformation that maps triangle ABC to triangle A'B'C' is a dilation centered at the origin (0, 0) with a scale factor of 0.5.