# if your given the midpoint= o,-3 and point A= 0,5 algebraically how do you find the other point?

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Given the midpoint M(0,-3) . One end point is A(0,5). To find the other end point.

Solution:

Given the end points whose coordinates are (x1,y1) and (x2,y2), the mid point is given by ( x1+x2)/2 , (y1+y2)/2. We use this idea when mid point and one end point is known is known.

So M(0,-3 ) = ((x1+x2)/2 , (y1+y2)/2)...(1) Given ( x1, y1) = A(0,5) . To determine (x2,y2). So substituting x1= 0 and y1 = 5 in eq(1), we get:

M(0,3) = ((0+x2)/2 , (5+y2)). Now equate x coordinates on both sides and also do so for y coordinates on both sides:

0 =(0+x2)/2 . Or **x2 = 0**

-3 =( 5+y2)/2. Or 5+y2 = -6. So **y2 = -6-5 = -11. **

**So (x2,y2) = (0,-11).**

The coordinates (x, y) of mid point 'C' of a line AB is given as:

x = (x1 + x2)/2 and

y = (y1 + y2)/2

Where coordinated of the points A and B are:

A(x1, y1) and B(x2, y2)

The question gives coordinates of the mid point (C) and on end of the line (A) as follows:

x = 0

y = -3

x1 = 0

y1 = 5

We have to find coordinates x2 and y2 of point B

x = (x1 + x2)/2

2x = x1 + x2

x2 = 2x - x1 = 2*0 - 0 = 0

Similarly:

y2 = 2y - y1 = 2*(-3) - 5 = - 6 - 5 = - 11

Answer:

The other point is: B(0, -11)

If we have a midpoint, this one is on the line formed with the points A(0,5) and B(xB,yB).

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

xB=2xM-xA, where xM=0 and xA=0

yB=2yM-yA, where yM=-3 and yA=5

Now, we just have to substitute the known values:

xB=2*0-0

**xB=0**

yB=2*(-3)-5

yB=-6-5

**yB=-11**

**The coordinates of the midpoint are: M(0,-11).**

Let the other point be (x,y)

Now, mid-point of (x,y) &(0,5) will be

[{(x+0)/2},{(y+5)/2}]

Given

{(x+0)/2} = 0

thus, x = 0

Also,

{(y+5)/2} = -3

or, y + 5 = -6

or, y = -11

Hence the required point (x,y) is (0,-11)