Question

Find the new triangle that undergoes a scale factor of 1.5 and a center of dilation at the origin

b=(4,-2)
a=(2,2)
c=(-4,-4)

Answer 1

To find the new triangle after applying a scale factor of 1.5 with a center of dilation at the origin, we need to multiply the coordinates of each vertex of the triangle by the scale factor.

The vertices of the original triangle are:
- \( A = (2, 2) \)
- \( B = (4, -2) \)
- \( C = (-4, -4) \)

We'll apply the scale factor of 1.5 to each vertex:

1. For vertex \( A \):
\[
A' = (1.5 \times 2, 1.5 \times 2) = (3, 3)
\]

2. For vertex \( B \):
\[
B' = (1.5 \times 4, 1.5 \times -2) = (6, -3)
\]

3. For vertex \( C \):
\[
C' = (1.5 \times -4, 1.5 \times -4) = (-6, -6)
\]

Thus, the coordinates of the new triangle after dilation are:
- \( A' = (3, 3) \)
- \( B' = (6, -3) \)
- \( C' = (-6, -6) \)

In summary, the new triangle vertices after the dilation are:
- \( A' = (3, 3) \)
- \( B' = (6, -3) \)
- \( C' = (-6, -6) \)