# Given the endpoint (2,-3) and the misdpoint (1,0.5), explain how to determine the other endpoint?

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### 3 Answers

The mid point of two points (x1, y1) and (x1, y2) is given by [(x1 + x2)/2, (y1 + y2)/2)]

Here we have one of the points as (2, -3) and the mid point is (1, 0.5)

If the other point is (x , y), we get:

(x + 2)/2 = 1

=> x = 1*2 - 2 = 0

(y - 3)/2 = 0.5

=> y = 2*0.5 + 3 = 4

**The other point is (0, 4)**

The given midpoint lies on the segment whose endpoints are P(2,-3) and N(xN,yN).

For finding the coordinates of the midpoint M(xM, yM), we have to solve the system:

xN=2xM-xP, where xM=1 and xP=2

yN=2yM-yP, where yM=1/2 and yP=-3

Now, we just have to substitute the known values:

xN=2*1-2

xN=0

yN=2*(1/2)-(-3)

yN = 1 + 3

yN=4

**The coordinates of the other endpoint of the segment whose midpoint is (1 , 1/2) are: (0,4).**

Let A(2,3) and B (x,y) be the end points.

Then the mid point coordinates are given by:

xM = (xA+XB)/2 and yM = (yA+yB)/2.

Substituting the given coordinates,xM = 1 and yM = 0.5, we get:

1 = (2+x)/2. So x = 2-2 = 0

0.5 = (-3+y)/2. So y = 1+3 = 4.

Therefore ** the other end point is B(x,y) = (0,4)**.