Given A=(x1,y1), B=(x2,y2), M midpt of AB, P of BC, Q of AC,

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suzanne

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Given: A= (x1, y1), B=(x2, y2)
M is the midpoint of Line AB.
P is the midpoint of Line BC.
Q is the midpoint of Line AC.
Prove:
A) P=( x2, y1+y2/2)

B) Q= (x1+x2/2, y1)

C) Points M and P have the same y-coordinate.
D) Points M and Q have the same x-coordinate.
E. M= (x1+x2/2, y1+y2/2)


Please explain, I'm totally lost
Thanks a bunch = )
 
Hi Suzanne:

After looking at what you need to prove, I can see that the coordinates of point C must be (x2, y1).

Here's a quick picture.

midpoint.JPG


However, if these coordinates for point C are not somehow given, then we cannot use them in our proofs. Are you sure that you posted ALL of the given information?

This entire exercise seems to be leading you towards confirmation of the midpoint formula. We can use the distance formula and geometric arguments with congruent triangles (eg: AMQ and MBP in my diagram) to work our way through these proofs. However, we cannot do any of these things until we're given enough information to know -- without peeking ahead -- that the coordinates of point C are as shown.

Cheers,

~ Mark
 
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