# Find the end point of the line segment AB . We know B(-2,12) and the midpoint which is ( 2,5) .

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the equation that relates the middle point located on a segment and the ends of the segment, such that:

`x = (x_A)/2 + (x_B)/2 => 2 = (x_A)/2 - 2/2`

`2 = (x_A)/2 - 1 => (x_A)/2 = 2 + 1 => (x_A)/2 = 3 => x_A = 6`

`y = (y_A)/2 + (y_B)/2 => 5 = (y_A)/2 + 12/2 => 5 = (y_A)/2 + 6`

`(y_A)/2 = 5 - 6 => (y_A)/2 = -1 => y_A = -2`

Hence, evaluating `x_A` and y_A of the point A, under the given conditions, yields `x_A = 6` and `y_A = -2` .

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

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).