The answers are written but I am not sure how they got them. Can someone please explain it to me? Thank you! (Worth 50 points :))

x = 2.4

I'm not sure how the answer is 4.5 but I'm pretty sure this is right unless I'm missing something

Step-by-step explanation:

So we need to find how much shorter is the short line compared to the longer one. Basically we need a scale factor, for this we can use the side lengths already given to us, 10 and 15. So u can choose either enlarge the short line or shorten the longer one.

If u want to enlarge the short line then do 15/10 which is 3/2 which u will then multiply the shorter line's equation with it, if u want to shorten the longer line then do 10/15 which is 2/3 and multiply the longer lines equation with it.

I'll be using the 3/2 one cause why not:

3/2(x + 6) = 4x + 3

3/2x + 18/2 = 4x + 3

multiply the entire equation with 2 to make 3/2 no longer a fraction

(3/2x + 18/2 = 4x + 3)2

6/2x + 18 = 8x + 6

3x + 18 = 8x + 6

subtract 18 from both sides

3x = 8x - 12

subtract 8x from both sides

-5x = - 12

divide -5 from both sides

x = 2.4

U can input x into the equation to check:

3/2(2.4 + 6) = 4(2.4) + 3

12.6 = 12.6, it's right

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.