Question

Find the new triangle that undergoes a scale factor of 3 and a center of dilation at the origin

b=(2,3)
a=(1,1)
c=(3,-1)

Answer 1

To find the new triangle after undergoing a dilation with a scale factor of 3 and a center of dilation at the origin, you need to multiply each coordinate of the vertices by the scale factor.

Given the vertices of the triangle:
- A = (1, 1)
- B = (2, 3)
- C = (3, -1)

We will apply the scale factor of 3 to each vertex:

1. For vertex A:
\[
A' = (3 \cdot 1, 3 \cdot 1) = (3, 3)
\]

2. For vertex B:
\[
B' = (3 \cdot 2, 3 \cdot 3) = (6, 9)
\]

3. For vertex C:
\[
C' = (3 \cdot 3, 3 \cdot (-1)) = (9, -3)
\]

Now, the new vertices of the triangle after dilation are:
- A' = (3, 3)
- B' = (6, 9)
- C' = (9, -3)

Thus, the new triangle is formed by the vertices:
- A' = (3, 3)
- B' = (6, 9)
- C' = (9, -3)