Apply Slope, Midpoint, and Length Formulas

This section shows you how to apply geometry and algebra to a variety of problems. Many of these problems involve several steps that require different skills. Developing a problem solving process is particularly important for dealing with such problems. These four steps can help you solve any multi-step problems:

1. Understand the problem.
2. Choose a strategy.
3. Carry out the strategy.
4. Reflect.

Find the Shortest Route

Question:   A ranger cabin is to be built in a flat wooded area near the straight road that connects the two campgrounds in a park. A new side road will connect the cabin to the campground road. On the park map, the campgrounds have coordinates  and , while the site for the cabin is at . Each unit on the map grid represents 500 m.

a) Find the route that minimizes the cost and the number of trees that have to be cut down for the side road. Draw a diagram of this route.

b) Find the length of the side road, to the nearest tenth of a kilometer.

Determine a Geometric Property Algebraically

Question: The vertices of ΔABC are A(5, 5), B(−3, −1), and C(1, −3).

a) Determine whether ΔABC is a right triangle.

b) Show that the median from the right angle of the triangle is half as long as the hypotenuse.