The coordinates for a rhombus are given as (2a,0), (0,2b), (-2a,0), and (0,-2b). Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Be sure to include the formulas

- annipuppi

- jamiebookeater

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- annipuppi

##### 1 Attachment

- myininaya

So you want the slopes of the intersecting line segments to be perpendicular, agreed?

- annipuppi

Yeah

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- myininaya

and I mean not the slopes to be perpendicular but the line segments to be perpendicular
i said that a little wrong
errr
but anyways the reason slopes came into mind is because we know what about the slopes if the line segments are perpendicular?

- annipuppi

They are the opposite recipricols and I knew what you meant haha

- myininaya

and i guess they were talking about the midpoints

- myininaya

not where the line segments intersect

- myininaya

|dw:1386186685552:dw|
pretend that is perfect

- myininaya

they already give you the midpoints

- myininaya

just show the slopes are undefined and 0 with those points given

- myininaya

like look at one line segment at a time
Take the line segment with (-a,b) and (-a,-b)

- myininaya

find the slope

- myininaya

then do the same with the line segment going through (-a,b) and (a,b)

- annipuppi

how do you find the slope of that though?

- myininaya

do you know the slope formula?
Also what do you know about the slopes of vertical lines and horizontal lines without using the slope formula?

- annipuppi

yeah and the slope of horizontal lines is 0 and the slope of vertical lines is undefined but how do we know they are horizontal and vertical lines?

- myininaya

all the points on x=a have what in common?

- myininaya

look at the line segment going through the midpoints

- annipuppi

oh I see now. nevermind that was a stupid question. Okay so now that I know the slopes of each line how do I prove its a rhombus?

- myininaya

you were trying to show that one thing is a rectangle

- annipuppi

oops I meant to say how do I prove its a rectangle

- myininaya

we did that by showing the angles were 90 degrees.

- myininaya

We show that by showing the line segments were perpendicular.

- myininaya

we knew the line segments were perpendicular because one was horizontal and the other was vertical

- myininaya

we knew we had a horizontal line segment because all the y values of the coordinates that lied on that line segment were the same

- annipuppi

Okay so there arent any formulas that I have to include or anything?

- myininaya

we knew we had a vertical line segment because all the x values of the coordinates that lied on that line segment were the same

- myininaya

If you want you could use that one formula I mentioned

- annipuppi

The slope formula right? but I don't really need it

- myininaya

You also might want to use that midpoint formula to show why those points in your picture are midpoints.

- annipuppi

Okay. that makes sense. Thanks for your help!

- myininaya

np

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