# Find the distance between points and the coordinates of the midpoint of the segment having the points as endpoints (3,3) and (-2,1) (-2,1) and (3,-2)No

*print*Print*list*Cite

As with circles, there is a set equation for the distance between two points. You can use it whenever you know the coordinates of the two points.

The distance formula is as follows:

distance = square root of (x2-x1)^2 + (y2-y1)^2

So it's the square root of that whole quantity. The x1 and x2, etc, should be subscripts but I don't know who to do those.

So for example, your first one would come out to

distance = square root of (3+2)^2 + (3-1)^2

That calculates out to square root of 25 + 4 or square root of 29

The process for finding out distance between midpoints of two line segments will be as follows:

- Find out the coordinates of the mid points.
- Find the distance between the two points thus defined by coordinates.

The formula for mid point for two pints represented by (x1, y1) and (x2, y2) is:

Mid point = ((x1+x2)/2, (y1+y2)/2)

and formula for distance between two points (x1, y1) and (x2, y2) is:

Distance = [(x1-x2)^2 + (y1-y2)^2]^1/2

**Solution:**

Midpoint of (3, 3) and (-2, 1):

= ((3-2)/2, (3+1)/2) = (0.5, 2):

And Midpoint of (-2, 1) and (3, -2)

= ((-2+3)/2, (1-2)/2) = (0.5, -0.5)

Distance between midpoints = distance between (0.5, 2) and (0.5, -0.5)

= [(0.5 - 0.5)^2 + (2 + 0.5)^2]^1/2 = (0 + 2.5^2)^1/2 = 2.5

**Note:**

When either x or y coordinates of two points are same, the distance between them is given by difference of the other coordinates.

The distance d between the points (x1,y1) and (x2,y2) is given by:

d = sqrt{(x1-x2)^2+(y1-y2)^2} and the coordinates of the mid point of the linesegment is [ (x1+x2)/2 , (y1+y2)/2 ]

Therefore, the distance between (3,3) and (-2,1) is

d = sqrt{(3--2)^2+(3-1)^2} = sqrt(25+4) = sqrt29 .

The coordinates of the mid points of the line segment from (3,3) to (-2,1) is { (3- -2)/2 , (3-1)/2 } = (5/2 , 1)

The distance between (-2,1) and (3,-2) is given by:

d = sqrt{(-2-3)^2+(1--2)^2} = sqrt{25+9} = sqrt34.

The coordinates of the mid points of the line segment from (-2,1) to (3,-2) is

[ (-2-3)/2 , (1- -2)/2 ] = (-5/2 , 3/2).