Question

Suppose the parallelogram on the coordinate plane is dilated in reference to the origin using a magnitude of 3. What would be the coordinates if the new vertices E(-1,5) F(2,8) G(4,4), H(1,1)

Answer 1

To dilate the vertices of a shape in reference to the origin using a dilation factor, you multiply each coordinate of the vertices by the dilation factor.

In this case, the dilation factor is 3, and the vertices of the parallelogram are:
- E(-1, 5)
- F(2, 8)
- G(4, 4)
- H(1, 1)

Now, let's apply the dilation factor to each vertex:

1. For vertex E(-1, 5):
\[
E' = (3 \times -1, 3 \times 5) = (-3, 15)
\]

2. For vertex F(2, 8):
\[
F' = (3 \times 2, 3 \times 8) = (6, 24)
\]

3. For vertex G(4, 4):
\[
G' = (3 \times 4, 3 \times 4) = (12, 12)
\]

4. For vertex H(1, 1):
\[
H' = (3 \times 1, 3 \times 1) = (3, 3)
\]

Thus, the new coordinates of the vertices after dilation are:
- E'(-3, 15)
- F'(6, 24)
- G'(12, 12)
- H'(3, 3)