Given two coordinates of a line as (x1, y1) and (x2, y2), find if the line passing through these points also passes through origin or not.
Input : (x1, y1) = (10, 0) (x2, y2) = (20, 0) Output : Yes The line passing through these points clearly passes through the origin as the line is x axis. Input : (x1, y1) = (1, 28) (x2, y2) = (2, 56) Output : Yes
Approach: Equation of a line passing through two points (x1, y1) and (x2, y2) is given by
y-y1 = ((y2-y1) / (x2-x1))(x-x1) + c
If line is also passing through origin, then c=0, so equation of line becomes
y-y1 = ((y2-y1) / (x2-x1))(x-x1)
Keeping x=0, y=0 in the above equation we get,
x1(y2-y1) = y1(x2-x1)
So above equation must be satisfied if any line passing through two coordinates (x1, y1) and (x2, y2) also passes through origin (0, 0).
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Improved By : jit_t