The municipal sewer line runs straight through a new subdivision from point A(20,20) to point B(80,60) on a survey map. Houses at C(30,70) and D(85,20) need connections to this sewer line. The developer calculates that connecting to the line at points E(50,40) and F(65,50) will minimize digging and the length of pipe required.
A) Verify that the developper has found the shortest route from each house to the sewer line.
B) to the nearest metre, what length of pipe is needed for the two connections if the intervals between grid lines on the survey each represent 2m?
C)the excavation contractor suggests digging a straight trench between the two houses and connecting to the sewer line at the point where the trench meets it. find the coordinates of this point,
D)should the developper use the contracter's suggestion? justify your answer.

This is a long problem not hard!!!
Find the eqn of AB. Show thatCE and DF are perpendiculars to AB, perpendicular is the shortest distance.
Rest is simple.
best way is to use a graph paper, plot the points and see it yourslef to believe it.