Thread: find the coordinate

hi,

this is my question:

the points A(1,2), B(3,5), C(6,6) and D form a parallelogram. Find the coordinates of the mid point of AC. use your answer to find the coordinates of D.

firstly i have found the mid points of AC which=(7,8)

secondly i don't really know how to use (7,8) to find the D coordinate.

Lastly i would really appreciate some help please, but could you really explain it so i understand!

thanks!

Originally Posted by andyboy179

hi,

this is my question:

the points A(1,2), B(3,5), C(6,6) and D form a parallelogram. Find the coordinates of the mid point of AC. use your answer to find the coordinates of D.

firstly i have found the mid points of AC which=(7,8) ... and this would be incorrect

secondly i don't really know how to use (7,8) to find the D coordinate.

Lastly i would really appreciate some help please, but could you really explain it so i understand!

thanks!

midpoint formula ...



Once you find the correct midpoint of AC, note that it is also the midpoint of BD because the diagonals of a parallelogram bisect each other.

so the correct midpoint now would =(3.5,4) however what would i do after this to find the coordinates of D?

Originally Posted by andyboy179

so the correct midpoint now would =(3.5,4) however what would i do after this to find the coordinates of D?

once again ...

Once you find the correct midpoint of AC, note that it is also the midpoint of BD because the diagonals of a parallelogram bisect each other.

i don't understand! i know that (3.5,4) is also the mid point of BD but what would D be? would it be (3.5,4)? would i be (7,8)? could you please explain?!

Originally Posted by andyboy179

i don't understand! i know that (3.5,4) is also the mid point of BD but what would D be? would it be (3.5,4)? would i be (7,8)? could you please explain?!

midpoint of BD ...



now ... what can you do with that?

do you mean, (3+x/2, 4+y/2) if so:

3x/2= 1.5x
4y/2= 2y
(1.5,2) ?

Continuing on the method skeeter provided:
The mid point of the line segment [AC] is and it's also the midpoint of [BD] therefore:
and
Solve this equations.

Originally Posted by Siron

Continuing on the method skeeter provided:
The mid point of the line segment [AC] is and it's also the midpoint of [BD] therefore:
and
Solve this equations.

3x/2= 1.5x
4y/2= 2y
(1.5,2) ?

Is ? Is ? I have no idea how you could possible get that. Have you never solved equations before? Start by multiplying each side of both those equations by 2.

6+x/2, 8+y/2

What you wrote now is not even an equation ...
If you have to solve:

Like HallsofIvy said, first multiply both sides with a factor 2, therefore we get:



Do this also for the other equation to find

oh sorry i mis read, i didn't see 3.5=!

7=3x
7/3= 2.3
2.3=x
-2.3 from each side x=-2.3?

You probably mean:

?

What do you get for ?

indeed, for y i got 3 so al together D=(4,3)