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annipuppi
 3 years 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
annipuppi
 3 years 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

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myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1So you want the slopes of the intersecting line segments to be perpendicular, agreed?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1and 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
 3 years ago
Best ResponseYou've already chosen the best response.0They are the opposite recipricols and I knew what you meant haha

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1and i guess they were talking about the midpoints

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1not where the line segments intersect

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1386186685552:dw pretend that is perfect

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1they already give you the midpoints

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1just show the slopes are undefined and 0 with those points given

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1like look at one line segment at a time Take the line segment with (a,b) and (a,b)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1then do the same with the line segment going through (a,b) and (a,b)

annipuppi
 3 years ago
Best ResponseYou've already chosen the best response.0how do you find the slope of that though?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1do 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
 3 years ago
Best ResponseYou've already chosen the best response.0yeah 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
 3 years ago
Best ResponseYou've already chosen the best response.1all the points on x=a have what in common?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1look at the line segment going through the midpoints

annipuppi
 3 years ago
Best ResponseYou've already chosen the best response.0oh 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
 3 years ago
Best ResponseYou've already chosen the best response.1you were trying to show that one thing is a rectangle

annipuppi
 3 years ago
Best ResponseYou've already chosen the best response.0oops I meant to say how do I prove its a rectangle

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1we did that by showing the angles were 90 degrees.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1We show that by showing the line segments were perpendicular.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1we knew the line segments were perpendicular because one was horizontal and the other was vertical

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1we 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
 3 years ago
Best ResponseYou've already chosen the best response.0Okay so there arent any formulas that I have to include or anything?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1we 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
 3 years ago
Best ResponseYou've already chosen the best response.1If you want you could use that one formula I mentioned

annipuppi
 3 years ago
Best ResponseYou've already chosen the best response.0The slope formula right? but I don't really need it

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

annipuppi
 3 years ago
Best ResponseYou've already chosen the best response.0Okay. that makes sense. Thanks for your help!
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