## anonymous 4 years ago ABCD is a square where A is the point (0,2) and C is the point (8,4). AC and BD are diagonals of the square and they intersect at E. Find the coordinates of B and D.

1. anonymous

I have found out the coordinate of E which is(4,3) and the equation of Bd and length of AE

2. amistre64

slope is 1/4?

3. amistre64

so perp slope is -4

4. anonymous

the ans for the coordinate of B is(5,-1) & D is (3,7)

5. anonymous

but i do not know how to derive at it

6. amistre64

the slope form a to c aint 1 so its not a square that situated nicely like that is it?

7. amistre64

slope from a to c is: 2/8 = 1/4

8. anonymous

ABCD is a square in the question

9. amistre64

e is a+c/2 for midpoint 8,4 0,2 ---- 8,6 /2 = 4,3 e is good

10. amistre64

y=-4x+4(4)+3 y=-4x+19 is the equation of the line perp to ac and thru 4,3

11. amistre64

hmmm, so. ; this laptop doesnt make this easier lol

12. amistre64

we need a vector that is the length of ae

13. anonymous

its $\sqrt{17}$ length of ae

14. amistre64

8,4 -4,3 ---- <4,1>; mag = sqrt(17) that ougt to be fun to play with

15. anonymous

i cant find a way to find the coordinate through the length of ae LOL

16. amistre64

so the vector representation of say eb is our -4/1 slope

17. amistre64

<1,-4> is out vector ... duh lol

18. amistre64

form e move 1,-4 and -1,4 to get to the other corners

19. anonymous

i was tinking of finding the coordinate through the x-axis difference and y-axis difference but it doesnt seem to work

20. amistre64

4,3 1,-4 ----- 5,-1 4,3 -1,4 ----- 3,7

21. anonymous

i get it thx:) alot

22. amistre64

took a bit my my brain clicked lol

23. Hero

So what were the correct points? For some reason, I'm getting (3,7) and (5,-1), but the question is which one is B and which one is D

24. anonymous

Hi im very sorry could you explain what is a vector?

25. amistre64

|dw:1327672189805:dw|

26. amistre64

a vector can be represented as a directed line segment; something like an arrow with distance and direction defines a vector

27. anonymous

how did u arrive at a vector of (-1,4)

28. amistre64

|dw:1327672246456:dw|

29. amistre64

the slope of a line IS its vector i took the slope of the line from A to C

30. amistre64

not drawn correctly in this pic, but same concept nonetheless

31. anonymous

gradient AC= 1/4 thus the vector is (-1,4 ) and gradient AB= 4 vector is (-4,1)?

32. amistre64

the slope of the line from A to C is: C (8,4) -A (0,2) -------- 8, 2 ; slope = 2/8; 1/4 the vector from A to C is then <4 , 1>

33. amistre64

a vector is notated the same as a point, except for the < > parts that indicate it as a vector. it is 4 wide and 1 tall; the components of its gradient (slope)

34. anonymous

How did u get C (8,4) -A (0,2) -------- 8, 2

35. amistre64

its called subtraction

36. amistre64

8-0 , 4-2 these are the parts of the slope formula

37. amistre64

its just easier for me to do them in this way then to try and sort out what goes where when its already done

38. amistre64

but to be clear about the vector from A to C, I was a little off in my explaining. The vector from A to C is actually <8,2>; half of this is going to be to the midpoint of E, since a midpoint is in the middle <8,2> ------ = <4,1>, is our vector from A to E 2

39. anonymous

i see thank you i will try to understand & do the question first, if I still do not understand could I still look for you? thx::)

40. amistre64

i might be around; it might be better to repost a new question, or even this one again so that others have a better chance to see it up on the left and give their views as well :)