# Midpoint

• Jan 17th 2008, 08:53 PM
Midpoint
Show that the midpoint of the line segment joining the points (a,b) and (c,d) is $( \frac {a+c}{2} , \frac {b+d}{2} )$

May be I'm just thinking too much, do I just simply use the midpoint formula here? Or do I have to do something more?
• Jan 17th 2008, 09:13 PM
CaptainBlack
Quote:

Show that the midpoint of the line segment joining the points (a,b) and (c,d) is $( \frac {a+c}{2} , \frac {b+d}{2} )$

May be I'm just thinking too much, do I just simply use the midpoint formula here? Or do I have to do something more?

You need to show that it is on the line between the points and that it is equidistant from both.

RonL
• Jan 17th 2008, 09:13 PM
ThePerfectHacker
Quote:

Show that the midpoint of the line segment joining the points (a,b) and (c,d) is $( \frac {a+c}{2} , \frac {b+d}{2} )$

May be I'm just thinking too much, do I just simply use the midpoint formula here? Or do I have to do something more?

1)Take for example (0,1) and (1,0) to illustrate.
2)Plot these point
3)Draw a line segment from (0,1) down and draw a line segment from (1,0) left.
4)Those intersect as (0,0)
5)By similar triangles if (x,y) is midpoint then x is midpoint of vertical line segment and y is midpoint of horizontal line segment.
• Jan 18th 2008, 04:41 AM
mr fantastic
Quote:

Show that the midpoint of the line segment joining the points (a,b) and (c,d) is $( \frac {a+c}{2} , \frac {b+d}{2} )$