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

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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

Mathematics
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yes, but its complicated :)
could you show me? thx alot!
since a square has diags that are perp to each other; we need 2 lines that meet in the middle of AC

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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
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
C (8,4) -A (0,2) ------- 8,2; stack y/x: 2/8 = 1/4 for our slope
perp slopes have the habit of being the negative reciprocal of each other. m1*m2 = -1
perp slope for th eline from B to D is then: -4/1
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
|dw:1327673742761:dw|
this is what weve got drawn up in out heads, or on paper
i know, this is where I had a brillant notion last time ... and I just remembered it :)
think of a pinwheel ....
|dw:1327674432861:dw|
our x and y parts for A to E are going to be swapped and negated for the perp from B to E
|dw:1327674563395:dw|
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
E (4,3) E (4, 3) +(-1,4) + (1,-4) ------ -------- B (3,7) D (5,-1)
that should clean up the right path a little better :)
i kind of get it from the pinwheel ting
ok thx:)
the pinwheel thing is a very good visual to guide us :)

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