## 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. Do you have any method other than using a vector

1. amistre64

yes, but its complicated :)

2. anonymous

could you show me? thx alot!

3. amistre64

since a square has diags that are perp to each other; we need 2 lines that meet in the middle of AC

4. amistre64

the slope of a line is the important part here; once we know the slope of the line from A to C we can determine other things

5. amistre64

the slope of a line is found by a slope formula:$m=\frac{y1-y2}{x1-x2}$ but i tend to step it out. 1) subtract the points 2) stack y/x

6. amistre64

C (8,4) -A (0,2) ------- 8,2; stack y/x: 2/8 = 1/4 for our slope

7. amistre64

perp slopes have the habit of being the negative reciprocal of each other. m1*m2 = -1

8. amistre64

perp slope for th eline from B to D is then: -4/1

9. amistre64

we need a common point for these to meet at, which is the middle of the square and hence E the midpoint is just the average of 2 other points. Add the points and divide by 2 C (8,4) +A (0,2) -------- (8,6)/2 = (4,3) as out point for E

10. amistre64

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11. amistre64

this is what weve got drawn up in out heads, or on paper

12. amistre64

i know, this is where I had a brillant notion last time ... and I just remembered it :)

13. amistre64

think of a pinwheel ....

14. amistre64

|dw:1327674432861:dw|

15. amistre64

our x and y parts for A to E are going to be swapped and negated for the perp from B to E

16. amistre64

|dw:1327674563395:dw|

17. amistre64

we know to go from A to E is over 4 and up 1 (x=4, y=1) these are the distances needed for the rest of them as well right? just perp them (x=1, y=-4) is our directions from E to D (x=-1, y=4) is our directions from E to B

18. amistre64

E (4,3) E (4, 3) +(-1,4) + (1,-4) ------ -------- B (3,7) D (5,-1)

19. amistre64

that should clean up the right path a little better :)

20. anonymous

i kind of get it from the pinwheel ting

21. anonymous

ok thx:)

22. amistre64

the pinwheel thing is a very good visual to guide us :)