# Determine the end point of the line segment AB if B(-2,12) and the midpoint is ( 2,5)

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Given the line segment AB such that B(-2, 12) and the midpoint m(2,5).

We need to find the coordinates of the point A.

We will use the midpoint formula to find A.

We know that:

xm = ( xA+xB)/2

==> 2 = (-2+xB)/2

Multiply by 2.

==> 4 = -2 + xB

==> xB = 4+2 = 6

==> xB = 6

Also we know that:

ym = (yA+yB)/2

==> 5 = (12 + yB)/2

==> (12+yB = 10

==> yB = -2

**Then, the point B is : B(6, -2) **

We know that the coordinates of the midpoint of a segment are the arithmetical mean of the endpoints of the segment:

xM = (xA + xB)/2

yM = (yA + yB)/2

But xM = 2 and yM = 5

2 = (xA - 2)/2

4 = xA - 2

We'll add 2 both sides:

xA = 6

5 = (yA + 12)/2

10 = yA + 12

We'll subtract 12 both sides:

yA = 10 - 12

yA = -2

**The coordinates of the other endpoint A are: A(6 ; -2).**