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Shortest distance from point to line

Assuming I have point (x, y) and line y=mx, I can find the shortest ppd distance between (x,y) and mx by creating a new line through (x,y) using the gradient -(1/m)

Is there a simple equation that tells me the x-coordinate of the intercept between these two lines?

Thank you

Reply 1

an_atheist

You would use the reciprocal of the gradient of the line -1/m as you said. For your given point (x,y), create a new equation with gradient -1/m, and then solve simultaneously to give a point of intersection. Once you have the point, use Pythagoras to find the distance
Not really sure if that answers the question, but that's the method I've always used and haven't come across anything simpler