Question

Triangle ABC was dilated using k=1/2 with a center of dilation at (7,0), then rotated 90° counter-clockwise around the point (-2,-3). Given are the slopes of the perpendicular bisectors for the 3 sides of the triangle: AB= -1/3, BC=3, AC = -2. Assume that counting rise/run from the point of concurrency once will land on the midpoint of those sides. If the circumcenter of triangle ABC is (-1,0), find the original coordinates of ABC.

Answer 1

To find the original coordinates of triangle ABC, we need to undo the two transformations: dilation and rotation. First, we undo the dilation by multiplying the coordinates of the dilated triangle by the reciprocal of the dilation factor. Then, we undo the rotation by applying the reverse rotation transformation. The original coordinates of triangle ABC are (-6, 14), (0, 14), and (0, 14).

Step-by-step explanation:

To find the original coordinates of triangle ABC, we need to undo the two transformations: dilation and rotation.

First, let's undo the dilation. Since the dilation factor is k = 1/2, the coordinates of the original triangle can be found by multiplying the coordinates of the dilated triangle by the reciprocal of the dilation factor. So the coordinates of the original triangle ABC are:

A' = (7*2, 0*2) = (14, 0)

B' = (7*2, -3*2) = (14, -6)

C' = (7*2, -6+3*2) = (14, 0)

Next, let's undo the rotation. We can do this by applying the reverse rotation transformation, which is a 90° clockwise rotation.

The coordinates of the original triangle after the rotation are:

A = (-6, 14)

B = (0, 14)

C = (0, 14)