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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

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

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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?
They are the opposite recipricols and I knew what you meant haha
and i guess they were talking about the midpoints
not where the line segments intersect
|dw:1386186685552:dw| pretend that is perfect
they already give you the midpoints
just show the slopes are undefined and 0 with those points given
like look at one line segment at a time Take the line segment with (-a,b) and (-a,-b)
find the slope
then do the same with the line segment going through (-a,b) and (a,b)
how do you find the slope of that though?
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?
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?
all the points on x=a have what in common?
look at the line segment going through the midpoints
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?
you were trying to show that one thing is a rectangle
oops I meant to say how do I prove its a rectangle
we did that by showing the angles were 90 degrees.
We show that by showing the line segments were perpendicular.
we knew the line segments were perpendicular because one was horizontal and the other was vertical
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
Okay so there arent any formulas that I have to include or anything?
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
If you want you could use that one formula I mentioned
The slope formula right? but I don't really need it
You also might want to use that midpoint formula to show why those points in your picture are midpoints.
Okay. that makes sense. Thanks for your help!
np

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