Select the correct answer. Triangle E'F'G' is the image of triangle EFG after a dilation with center at (2-3).
What is the scale factor of this dilation?
A: 2
B: 3
C: 1/2
D: 1/3

Explanation:

Start at (2,-3). Move up 3 and over to the right 6 spots to move to (8,0) which is where point F is located.

We can write the slope as rise/run = 3/6

Go back to (2,-3). Move up 1 and to the right 2 spots to arrive at F ' (4,-2)

Let's now compare the upward movements:

The starting point each time is (2,-3) which is the center of dilation. The jump from 3 to 1 is "times 1/3" and that's our scale factor. Every linear distance in the image is 1/3 times as long compared to the preimage.

We can also get the same scale factor when comparing the horizontal movements as well. The jump from 6 to 2 is also "times 1/3".

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .