Question

Find the new triangle that undergoes a scale factor of 2.5 and a center of dilation at the origin

b=(0,0)
a=(-2,-2)
c=(2,-4)

Answer 1

To apply a scale factor of 2.5 and a center of dilation at the origin to each point of the triangle with vertices \( B = (0, 0) \), \( A = (-2, -2) \), and \( C = (2, -4) \), we can use the formula for dilation:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the scale factor.

Given that the scale factor \( k = 2.5 \):

1. For point \( A = (-2, -2) \):
\[
x' = 2.5 \cdot (-2) = -5
\]
\[
y' = 2.5 \cdot (-2) = -5
\]
So, the new point \( A' = (-5, -5) \).

2. For point \( B = (0, 0) \):
\[
x' = 2.5 \cdot 0 = 0
\]
\[
y' = 2.5 \cdot 0 = 0
\]
So, the new point \( B' = (0, 0) \).

3. For point \( C = (2, -4) \):
\[
x' = 2.5 \cdot 2 = 5
\]
\[
y' = 2.5 \cdot (-4) = -10
\]
So, the new point \( C' = (5, -10) \).

Thus, the coordinates of the new triangle after the dilation by a scale factor of 2.5 about the origin are:

- \( A' = (-5, -5) \)
- \( B' = (0, 0) \)
- \( C' = (5, -10) \)