Question

Parallelogram with vertices A(-2, -1), B (-3, 2), C (1, 3), and D (2, 0) is drawn on a coordinate grid.



Suppose the parallelogram is dilated in reference to the origin using a magnitude of 2.



What would be the coordinates of the new vertices A'B'C'D'?

Answer 1

To find the new coordinates of the vertices of the parallelogram after dilating with respect to the origin by a magnitude of 2, we multiply the coordinates of each vertex by 2.

The original vertices are:

- A(-2, -1)
- B(-3, 2)
- C(1, 3)
- D(2, 0)

Now we will dilate each vertex:

1. For A(-2, -1):
\[
A' = (2 \times -2, 2 \times -1) = (-4, -2)
\]

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

3. For C(1, 3):
\[
C' = (2 \times 1, 2 \times 3) = (2, 6)
\]

4. For D(2, 0):
\[
D' = (2 \times 2, 2 \times 0) = (4, 0)
\]

Thus, the coordinates of the new vertices A', B', C', and D' after dilation are:
- A'(-4, -2)
- B'(-6, 4)
- C'(2, 6)
- D'(4, 0)