Question

HELP!!!!!!!!! Given the following endpoint (A) and midpoint (M), find the other endpoint (B).
M(2, 3)
A(0, -1)

Answer 1

You know that M is the midpoint between A and the other point, so that means it is halfway there. How much does the x and y change from the endpoint to the midpoint?

Answer 2

2,2?

Answer 3

Look at the individual x and y parts of the ordered pairs:

(2,3), x=2 y=3
(0,-1), x=0 y=-1

How much does x change by and how much does y change by between these points?

Answer 4

I dont get it . do i supposed to subtract or what ?

Answer 5

You find the difference between each of the x's and each of the y's. So yes you'd find the difference.

Answer 6

2-0 = 2 3-(-1) = 2

Answer 7

3-(-1) is actually 4, be careful with that

Answer 8

so it will be (2,4)

Answer 9

But yes now you found the change in x and the change in y. Since that is the change from the beginning to the midpoint, the other endpoint will be twice as far. Could you tell me what you think needs to be done now?

Answer 10

multiply by 2 ?

Answer 11

And the 2 and 4 are actually just vector quantities, don't worry about what that means yet but it's not used to make a point.

Answer 12

And yes, you multiply by 2. What new point does that give us?

Answer 13

4,8 ?

Answer 14

No, multiply the 2 and 4 by 2, and then use that new change in x and y to find the new point

Answer 15

4 is the change in x and 8 is the change in y from the initial starting point, so what's the point on the other end?

Answer 16

4,7 ?

Answer 17

Im really confused

Answer 18

Yep! That point is twice as far as the midpoint correct?

Answer 19

Because the x and y changes by twice as much

Answer 20

Ok I get it. THANK YOU!!! :)

Answer 21

Haha I'm glad you understand now ^^