Exercise 27 Page 557

To find the minimum distance, we can reflect one of the points representing a house in line n and then connect it to the point representing the other house. Where this new segment intersects line n, is where you should park the car to minimize the distance you have to walk. Let's do a reflection of J in line n.

Finally, we will draw HJ'. Where this segment intersects line n, is where we should park our car to minimize the distance.

Since HJ' is the shortest distance between H and J' and KJ=KJ', then parking at point K minimizes the distance HK+JK.