1. ## 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)

2. 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)

Please for the love of god help me........

As for the answer, find the equation of the lines of 2 pairs of points, and then find where the two lines intersect.

3. Pardon my language, completely out of line....

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

4. 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.

5. 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 $\displaystyle P_1(x_1, y_1)$and $\displaystyle P_2(x_2, y_2)$ then the midpoint has the ccordinates:

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

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

6. 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 $\displaystyle P_1(x_1, y_1)$and $\displaystyle P_2(x_2, y_2)$ then the midpoint has the ccordinates:

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

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

7. 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:

8. 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...

9. 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.

10. 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 ... ...ok. so i think drawing a rough sketch is good enough, then we will know what points to test using Earboth's method

11. 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 ... ...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.

12. 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!)

13. 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...
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.
Originally Posted by Jhevon