# Parallelograms

• March 23rd 2008, 09:24 AM
TheTruePhenom
Parallelograms
OK, I am learning about Parallelograms at the moment and I am stuck on a certain problem....

COORDINATE GEOMETRY Find the coordinates of the intersection of the diagonals of parallelograms PRYZ given each set of vertices.

P(2,5) R(3,3) Y(-2,-3) Z(-3,-1)

• March 23rd 2008, 09:30 AM
janvdl
Quote:

Originally Posted by TheTruePhenom
OK, I am learning about Parallelograms at the moment and I am stuck on a certain problem....

COORDINATE GEOMETRY Find the coordinates of the intersection of the diagonals of parallelograms PRYZ given each set of vertices.

P(2,5) R(3,3) Y(-2,-3) Z(-3,-1)

As for the answer, find the equation of the lines of 2 pairs of points, and then find where the two lines intersect.
• March 23rd 2008, 09:33 AM
TheTruePhenom
Pardon my language, completely out of line....

I dont understand by what you mean.....
• March 23rd 2008, 09:37 AM
janvdl
Quote:

Originally Posted by TheTruePhenom
I dont understand by what you mean.....

You have 4 points... Make 2 pairs of 2 points. Find the y = mx + c line between each of these pairs. You will then have the formulae of the diagonals. To find out where they intersect, set the formulae equal to each other.
• March 23rd 2008, 09:47 AM
earboth
Quote:

Originally Posted by janvdl
You have 4 points... Make 2 pairs of 2 points. Find the y = mx + c line between each of these pairs. You will then have the formulae of the diagonals. To find out where they intersect, set the formulae equal to each other.

A happy Easter to you!

In this case it's a little bit easier to use the property that the point of intersection of the diagonals must be the midpoint of the diagonals:

If you have 2 points $P_1(x_1, y_1)$and $P_2(x_2, y_2)$ then the midpoint has the ccordinates:

$M_{P_1 P_2}\left(\frac{x_1+x_2}2,\frac{y_1+y_2}2,\right)$

$M_{PY}\left(0,1\right)$
• March 23rd 2008, 09:49 AM
janvdl
Quote:

Originally Posted by earboth
A happy Easter to you!

In this case it's a little bit easier to use the property that the point of intersection of the diagonals must be the midpoint of the diagonals:

If you have 2 points $P_1(x_1, y_1)$and $P_2(x_2, y_2)$ then the midpoint has the ccordinates:

$M_{P_1 P_2}\left(\frac{x_1+x_2}2,\frac{y_1+y_2}2,\right)$

$M_{PY}\left(0,1\right)$

A happy Easter to you too, Earboth! :)

(I always take the long way... Not because I'm hardworking, just because I fail to see the shortcut) :D
• March 23rd 2008, 10:18 AM
CaptainBlack
Quote:

Originally Posted by TheTruePhenom
Pardon my language, completely out of line....

I dont understand by what you mean.....

You don't need "for the love of anything" especially as it may offend some
of our uses unnecessarily.

Ron:
• March 23rd 2008, 10:19 AM
TheTruePhenom
I think I have the hang of it. I was using the slope formula instead of the midpoint formula and that got me all twisted around.....

What about something of this extent....

COORDINATE GEOMETRY Determine whether a figure with the given vertices is a parallelogram. Use the Method INdicated:

P(-5,1) S(-2,2) F(-1,-3) T(2,-2) ; Slope Formula...
• March 23rd 2008, 11:39 AM
Mathnasium
Remember that a parallelogram is defined by the fact that it has two pairs of parallel sides. NOW is the time for the slope formula - find the slopes of all four lines. If the slopes of each pair of opposite sides are the same, then you have two sets of parallel sides and, hence, a parallelogram.
• March 23rd 2008, 11:51 AM
Jhevon
Quote:

Originally Posted by Mathnasium
Remember that a parallelogram is defined by the fact that it has two pairs of parallel sides. NOW is the time for the slope formula - find the slopes of all four lines. If the slopes of each pair of opposite sides are the same, then you have two sets of parallel sides and, hence, a parallelogram.

we are given that it is a parallelogram, we don't have to prove that. we trust the people giving us our question ...(Thinking) ...ok. so i think drawing a rough sketch is good enough, then we will know what points to test using Earboth's method
• March 23rd 2008, 12:15 PM
Mathnasium
Quote:

Originally Posted by Jhevon
we are given that it is a parallelogram, we don't have to prove that. we trust the people giving us our question ...(Thinking) ...ok. so i think drawing a rough sketch is good enough, then we will know what points to test using Earboth's method

I was referring to the question in the post immediately above mine - the original post was answered. The post immediately above mine, as you can see, is about proving that 4 given points are vertices of a parallelogram using the slope method.

Thanks for the snark, though.
• March 23rd 2008, 01:02 PM
Jhevon
Quote:

Originally Posted by Mathnasium
I was referring to the question in the post immediately above mine - the original post was answered. The post immediately above mine, as you can see, is about proving that 4 given points are vertices of a parallelogram using the slope method.

Thanks for the snark, though.

i didn't realize a second question was asked

(jeez, i'm turning into an american with that "my bad" stuff!)
• March 23rd 2008, 06:58 PM
topsquark
Quote:

Originally Posted by TheTruePhenom
I think I have the hang of it. I was using the slope formula instead of the midpoint formula and that got me all twisted around.....

What about something of this extent....

COORDINATE GEOMETRY Determine whether a figure with the given vertices is a parallelogram. Use the Method INdicated:

P(-5,1) S(-2,2) F(-1,-3) T(2,-2) ; Slope Formula...

Quote:

Originally Posted by Mathnasium
I was referring to the question in the post immediately above mine - the original post was answered. The post immediately above mine, as you can see, is about proving that 4 given points are vertices of a parallelogram using the slope method.

Thanks for the snark, though.

Quote:

Originally Posted by Jhevon