Analytical Geometry Question Which May Require Using a Graph

Question

A playground (R) is to be built near a straight path that connects a baseball diamond (A) and a basketball court (B). A new side path will connect the playground to the road that currently exists between A and B. On the park map, the baseball diamond and the basketball court have coordinates A(1.0, 5.0) and B(4.0, 2.0), while the site for the new playground is at R(2.0, 1.0).

Find an equation that represents the route that minimizes the cost for this new road.

Answer 1

What you are being asked here is what is the shortest distance between point R and the line between A and B.

The answer is the perpendicular distance between the point and the line.

To answer the problem:

You need the slope of the line.

The slope of the perpendicular will be the negative reciprocal of this slope.

Now use the point slope form to get the equation of the line through R and perpendicular to AB.

I think you should be able to answer this problem with that information.