A home in rural area located at A (22,-24) IS CONVERTING TO NATURAL GAS HEATING. They will be connecting the home to a main gas line with the end points G (-16,-30) and H (38,42) Each unit represents 1m. At what point should the builder connect to the main gas lines to minimize cost.

Question

A home in rural area located  at A (22,-24) IS CONVERTING TO NATURAL GAS HEATING. They will be connecting the home to a main gas line with the end points G (-16,-30) and H (38,42) Each unit represents 1m. At what point should the builder connect to the main gas lines to minimize cost.

Reiny · Answer

Find the general equation of the line through G and H, using
your favourite method.

You want the shortest distance from point A to the line you found

If the coordinates of a point are (a,b)
then the shortest distance to Ax + By + C = 0
= |aA + bB + C|/√(A^2 + B^2)

once you have the equation, just plug in and grind it out

Anonymous · Answer

Alright I found the answer I believe. Thanks