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

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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

 

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

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

  1. Find out the coordinates of the mid points.
  2. 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.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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).

 

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