Question

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

Answer 1

yes, but its complicated :)

Answer 2

could you show me? thx alot!

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

think of a pinwheel ....

Answer 13

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