Vectors

We have orthogonal vectors when their dot products  = 0

So

(2, 1) dot (-3, 6)  =  -6 +6  =  0    orthogonal

(2, 1) dot (  1, 2 )  = 2 + 2   = 4    not  orthogonal

(2, 1) dot ( -2, - 3)  = -4 + -3  =  -7     not orthogonal

(2, 1) dot ( 1, - 2)  = 2 + -2  =  0       orthogonal

[ I'm assuming that your are familiar with dot products ....]

Similarly.....treat   2,1 as a vector    slope = rise/run =   1/2       orthoganal slope is -2

-3,6     rise / run =   6/-3 = -2    orthogonal

1,2     2/1 = 2    nope

-2,-3     -3/-2     nope

1, -2     -2/1     orthogonal