Question

I need some help with writing this coordinate proof... :c

Answer 1

I know the distance/slope/midpoint formulas, but I'm still kind of confused. :c

Answer 2

find the slope of WY and XZ. If they are perpendicular, they should have slopes that have a product of -1.

Slope formula is rise/run.

Answer 3

find slope of the line wy and zx, let it be m1 and m2
let two points be x2,y2 and x1,y1
slope m=(y2-y1)/(x2-x1)
slope of line wy=(4b-0)/(a-a)=infinity
slope of line zx=(b-b)/(0-2a)=0
now find tan inverse of each slope that will give us the angle the line makes with the x axis
tan inverse of infinity is 90 degrees
tan inverse of 0 is 0 degrees
so wy is perpendicular to x axis
and zx is parallel to x axis
so wy is perpendicular to zx
hence the diagonals are perpendicular to each other

Answer 4

@Ash: Precisely. Although a very complicated proof, I can see. :P

Answer 5

Thank you so much! That helps a lot. :D

Answer 6

To show in a general way that two lines intersect at 90 degrees can be done by expressing each line in its general form: Ax+By+C=0
Say we have two lines,
L1 : 5x+2y-5=0, and
L2 : -4x + 10y +7=0
If the products of corresponding coefficients of x and y add up to zero, then the two lines intersect at 90 degrees.
In the cited example, we find
5(-4)+2(10)=0, so we can safely conclude that L1 is perpendicular (orthogonal) to L2.
This result comes from linear algebra or vector products.

The best part is that the test still works with vertical and horizontal lines:
L3 : x - a = 0
L4 : + y - b = 0
Then since
1(0)+0(1)=0, L3 is perpendicular to L4.