1. ## 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!

2. ## Re: find the coordinate

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.

3. ## 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?

4. ## Re: find the coordinate

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.

5. ## 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?!

6. ## Re: find the coordinate

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?

7. ## 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) ?

8. ## 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.

9. ## Re: find the coordinate

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) ?

10. ## 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.

6+x/2, 8+y/2

12. ## 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 $\displaystyle y$

13. ## 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?

14. ## Re: find the coordinate

You probably mean:
$\displaystyle 7=3+x \Leftrightarrow x=4$
?

What do you get for $\displaystyle y$?

15. ## Re: find the coordinate

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

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