## annipuppi one year 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

1. annipuppi

2. myininaya

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

3. annipuppi

Yeah

4. 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?

5. annipuppi

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

6. myininaya

and i guess they were talking about the midpoints

7. myininaya

not where the line segments intersect

8. myininaya

|dw:1386186685552:dw| pretend that is perfect

9. myininaya

they already give you the midpoints

10. myininaya

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

11. myininaya

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

12. myininaya

find the slope

13. myininaya

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

14. annipuppi

how do you find the slope of that though?

15. 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?

16. 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?

17. myininaya

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

18. myininaya

look at the line segment going through the midpoints

19. 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?

20. myininaya

you were trying to show that one thing is a rectangle

21. annipuppi

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

22. myininaya

we did that by showing the angles were 90 degrees.

23. myininaya

We show that by showing the line segments were perpendicular.

24. myininaya

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

25. 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

26. annipuppi

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

27. 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

28. myininaya

If you want you could use that one formula I mentioned

29. annipuppi

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

30. myininaya

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

31. annipuppi

Okay. that makes sense. Thanks for your help!

32. myininaya

np

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