How are x axis and y axis perpendicular if product of their slopes is not equal to -1?

Answer 1

let (C,0) be a point on the positive x-axis and (0,k) be a point on the positive y-axis

The triangle formed by these 2 points and the origin has legs C and k

The distance between them is sqrt (C^2 + k^2)

These points satisfy the pythagorean theorem, which means

the triangle is a RIGHT triangle which forces the angle

at the origin to be a right angle.

Therefore they are perpendicular