# What is the end point of the segment MN if N(-1;11) and the midpoint of the segment is (1;5) ?

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We have the coordinates of the point N as (-1 , 11). Let the coordinates of M be (x, y). The mid point of M and N has the coordinates (1, 5)

We know that the mid point of (x1, y1) and (x2, y2) is [(x1 + x2)/2, (y1 + y2)/2]

So we can write the equations:

(-1 + x)/2 = 1 and (11 + y)/2 = 5

=> -1 + x = 2 and 11 + y = 10

=> x = 3 and y = -1

**The coordinates of M are (3 , -1)**

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

xA = (xM + xN)/2

yA = (yM + yN)/2

But xA = 1 and yA = 5

1 = (xM - 1)/2

2 = xM - 1

We'll add 1 both sides:

xM = 3

5 = (yM+ 11)/2

10 = yM + 11

We'll subtract 11 both sides:

yM = 10 - 11

yM = -1

**The coordinates ****of the endpoint M are: A(3 ; -1).**