Make a diagram. What are the possible routes the plane can take?
165 units. Flying T to V, then to U, is the shortest distance.
Practice makes perfect
Let's begin with graphing T, U, and V on a coordinate plane. There are two possible ways in which the plane can fly to both U and V from the point T. We show them in the diagram below.
Now we can answer the questions from the exercise.
What information is needed to find the shortest possible distance?
To find the shortest possible distance, we have to determine which of the routes is shorter. To do it, let's find the distances between the given points using the Distance Formula.
Points
Substitute in Distance Formula
Simplify
T and V
sqrt((110-80)^2+(85-20)^2)
≈ 71.6
V and U
sqrt((110-20)^2+(85-60)^2)
≈ 93.4
T and U
sqrt((80-20)^2+(20-60)^2)
≈ 72.1
Next, let's calculate the distance the plane would fly taking Route I and Route II.
Route I
As we can see in our diagram, Route I leads from point T to point V first, and then to point U. Therefore, from the table we can calculate its distance by adding the distances between these points together.
71.6+93.4=165
Route II
Route II leads from point T to point U first, and then to point V. Again, let's find the distance by adding the distances between these points!
72.1+93.4=165.5
As we can see, Route I is shorter! Thus, the shortest possible distance is 165 units.
How can a diagram help?
A diagram can help us to see how the points are located in respect to each other. Then, it is easier to see the possible routes the plane can take.
