Question

A line is written in the form Ax+By=0, where A and B are not both zero. Find the coordinates of the point that must lie on this line, no matter what the choice of A and B

Answer 1

(x, -(A/B)*x)

Explanation:

We have the line:

A*x + B*y = 0

And we want to find the coordinates of the point that lie on this line.

Where the coordinates of a point P are written as (x, y)

The first step to do this, is to write the line in a more general way, we can do this by isolating y in the left side of the equation:

A*x + B*y = 0

B*y = -A*x

y = -(A/B)*x

Now, for a random point (x, y), if we replace the "y" by the equation above, we know that the point will also lie on the line.

This means that the coordinates of the points that lie on the line are of the form:

P = (x, -(A/B)*x)