# find the coordinate

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• Sep 23rd 2011, 07:49 AM
andyboy179
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!
• Sep 23rd 2011, 09:33 AM
skeeter
Re: find the coordinate
Quote:

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 ...

$\displaystyle (x_m,y_m) = \left(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2}\right)$

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.
• Sep 23rd 2011, 10:09 AM
andyboy179
Re: find the coordinate
so the correct midpoint now would =(3.5,4) however what would i do after this to find the coordinates of D?
• Sep 23rd 2011, 10:25 AM
skeeter
Re: find the coordinate
Quote:

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 ...

Quote:

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.
• Sep 23rd 2011, 10:30 AM
andyboy179
Re: find the coordinate
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?!
• Sep 23rd 2011, 10:39 AM
skeeter
Re: find the coordinate
Quote:

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?!

$\displaystyle B(3,5)$ $\displaystyle D(x,y)$

midpoint of BD ...

$\displaystyle (3.5,4) = \left(\frac{3+x}{2} , \frac{5+y}{2}\right)$

now ... what can you do with that?
• Sep 23rd 2011, 10:44 AM
andyboy179
Re: find the coordinate
do you mean, (3+x/2, 4+y/2) if so:

3x/2= 1.5x
4y/2= 2y
(1.5,2) ?
• Sep 23rd 2011, 11:03 AM
Siron
Re: find the coordinate
Continuing on the method skeeter provided:
The mid point of the line segment [AC] is $\displaystyle (3,5;4)$ and it's also the midpoint of [BD] therefore:
$\displaystyle 3,5=\frac{3+x}{2}$ and $\displaystyle 4=\frac{5+y}{2}$
Solve this equations.
• Sep 23rd 2011, 11:21 AM
andyboy179
Re: find the coordinate
Quote:

Originally Posted by Siron
Continuing on the method skeeter provided:
The mid point of the line segment [AC] is $\displaystyle (3,5;4)$ and it's also the midpoint of [BD] therefore:
$\displaystyle 3,5=\frac{3+x}{2}$ and $\displaystyle 4=\frac{4+y}{2}$
Solve this equations.

3x/2= 1.5x
4y/2= 2y
(1.5,2) ?
• Sep 23rd 2011, 11:57 AM
HallsofIvy
Re: find the coordinate
Is $\displaystyle \frac{3+1.5}{2}= 3.5$? Is $\displaystyle \frac{4+ 2}{2}= 4$? 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.
• Sep 23rd 2011, 12:02 PM
andyboy179
Re: find the coordinate
6+x/2, 8+y/2
• Sep 23rd 2011, 12:10 PM
Siron
Re: find the coordinate
What you wrote now is not even an equation ...
If you have to solve:
$\displaystyle 3,5=\frac{3+x}{2}$
Like HallsofIvy said, first multiply both sides with a factor 2, therefore we get:
$\displaystyle 2(3,5)=2\left(\frac{3+x}{2}\right)$
$\displaystyle \Leftrightarrow x=...$

Do this also for the other equation to find $\displaystyle y$
• Sep 23rd 2011, 12:13 PM
andyboy179
Re: find the coordinate
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?
• Sep 23rd 2011, 12:45 PM
Siron
Re: find the coordinate
You probably mean:
$\displaystyle 7=3+x \Leftrightarrow x=4$
?

What do you get for $\displaystyle y$?
• Sep 23rd 2011, 12:51 PM
andyboy179
Re: find the coordinate
indeed, for y i got 3 so al together D=(4,3)
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