Question

The parallelogram E'F'G'H' is a dilation of the parallelogram EFGH. What is the scale factor of the dilation?
E= 1,2
F= -1,1
G= -1,-2
H= 1,-1

E'= 4,8
F'= -4,4
G'= -4,-8
H'= 4, -4

Answer 1

To find the scale factor of the dilation from the parallelogram EFGH to the parallelogram E'F'G'H', we can use the coordinates of corresponding points in the two parallelograms.

Given points:
- E (1, 2) and E' (4, 8)
- F (-1, 1) and F' (-4, 4)
- G (-1, -2) and G' (-4, -8)
- H (1, -1) and H' (4, -4)

The scale factor \( k \) can be calculated using the formula:

\[
k = \frac{\text{distance from the center of dilation to E'}}{\text{distance from the center of dilation to E}}
\]

We can also calculate the scale factor by using the corresponding coordinates directly.

Let's calculate it for point E and E':

\[
k = \frac{E'x}{Ex} = \frac{4}{1} = 4
\]

Now for point F and F':

\[
k = \frac{F'x}{Fx} = \frac{-4}{-1} = 4
\]

For point G and G':

\[
k = \frac{G'x}{Gx} = \frac{-4}{-1} = 4
\]

For point H and H':

\[
k = \frac{H'x}{Hx} = \frac{4}{1} = 4
\]

In each case, the scale factor \( k \) is 4. Therefore, the scale factor of the dilation is:

\[
\boxed{4}
\]