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

Question

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): $$A^{\prime }=(2\times -2,2\times -1)=(-4,-2)$$

2. For B(-3, 2): $$B^{\prime }=(2\times -3,2\times 2)=(-6,4)$$

3. For C(1, 3): $$C^{\prime }=(2\times 1,2\times 3)=(2,6)$$

4. For D(2, 0): $$D^{\prime }=(2\times 2,2\times 0)=(4,0)$$

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)