The midpoint of Line Segment AB is (2,-9). The coordinates of one endpoint are A(4,10). Find the coordinates of endpoint B.

Question

Can someone please check my work and tell me if my answer is correct.

Step 1:
2x-9= 4x+10
2x-9= 10
2x= 1

Step 2:
AB= 2x-9
=2(1)-9
=-18
--------------------------------------------A= 4x+ 10
=4(1)+ 10
= 40

Step 3:
AB= AB+ A
=-18+ 40
= 22

Answer: AB and A are both -18. B is 22.

Answer 1

Rubbish. Did you actually plot the points?

Let's call the midpoint M. M is just as far from A as it is from B. So, if you consider the coordinates,

M-A = B-M
Or, B = 2M-A = 2(2,-9)-(4,10) = (4,-18)-(4,10) = (0,-28)

Or, in other words, moving from A to M caused x to go from 4 to 2. Continuing on an equal distance to B, x decreases by 2 again, making B's x-coordinate = 0. Similarly for y: It is 19 units from 10 to -9. Moving down another 19 gives -28.