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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
 4 months ago
 4 months ago
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
 4 months ago
 4 months ago

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myininayaBest ResponseYou've already chosen the best response.1
So you want the slopes of the intersecting line segments to be perpendicular, agreed?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
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?
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
They are the opposite recipricols and I knew what you meant haha
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
and i guess they were talking about the midpoints
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
not where the line segments intersect
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
dw:1386186685552:dw pretend that is perfect
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
they already give you the midpoints
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
just show the slopes are undefined and 0 with those points given
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
like look at one line segment at a time Take the line segment with (a,b) and (a,b)
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
then do the same with the line segment going through (a,b) and (a,b)
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
how do you find the slope of that though?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
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?
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
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?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
all the points on x=a have what in common?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
look at the line segment going through the midpoints
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
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?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
you were trying to show that one thing is a rectangle
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
oops I meant to say how do I prove its a rectangle
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
we did that by showing the angles were 90 degrees.
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
We show that by showing the line segments were perpendicular.
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
we knew the line segments were perpendicular because one was horizontal and the other was vertical
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
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
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
Okay so there arent any formulas that I have to include or anything?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
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
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
If you want you could use that one formula I mentioned
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
The slope formula right? but I don't really need it
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
You also might want to use that midpoint formula to show why those points in your picture are midpoints.
 4 months ago

annipuppiBest ResponseYou've already chosen the best response.0
Okay. that makes sense. Thanks for your help!
 4 months ago
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