Question

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

Answer 1

To dilate a point \((x, y)\) in reference to the origin by a factor of \(k\), you can use the formula:

\[
(x', y') = (kx, ky)
\]

Given the dilation factor of \(3\), we will multiply the coordinates of each vertex of the parallelogram by \(3\).

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

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

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

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

Now, the new vertices after dilation are:

- \(E'(-3, 15)\)
- \(F'(6, 24)\)
- \(G'(12, 12)\)
- \(H'(3, 3)\)

So the coordinates of the new vertices \(E'F'G'H'\) are \((-3, 15)\), \((6, 24)\), \((12, 12)\), and \((3, 3)\).