Question

Triangle ABC coordinates are: A: (-2,-5) B: (0,3) C: (6,-3)
A triangle is drawn on a coordinate plan. Dilate the figure with a magnitude of 3 in reference to the origin. What are the coordinates of the new vertices of A'B'C'?

Answer 1

To dilate a triangle from the origin with a magnitude of \(k\), you multiply the coordinates of each vertex by \(k\). In this case, the magnitude of the dilation is 3.

Given the coordinates of triangle ABC:
- A: \((-2, -5)\)
- B: \((0, 3)\)
- C: \((6, -3)\)

We will calculate the coordinates for the new vertices A', B', and C' as follows:

1. For vertex A:
\[
A' = (3 \cdot -2, 3 \cdot -5) = (-6, -15)
\]

2. For vertex B:
\[
B' = (3 \cdot 0, 3 \cdot 3) = (0, 9)
\]

3. For vertex C:
\[
C' = (3 \cdot 6, 3 \cdot -3) = (18, -9)
\]

Thus, the coordinates of the new vertices after dilation are:
- A': \((-6, -15)\)
- B': \((0, 9)\)
- C': \((18, -9)\)

In summary, the coordinates of the new vertices A', B', and C' are:
- A': \((-6, -15)\)
- B': \((0, 9)\)
- C': \((18, -9)\)