An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip?

Question

mathmate · Answer

Compare the distances T-U-V  and T-V-U and take the shorter of the two.

lime · Answer

$$\sqrt((20 - 60)^2 + (80 - 20)^2)$$
$$\sqrt((-40)^2 + 60^2)$$
$$\sqrt(1600 + 3600)$$
$$\sqrt(5200)$$

lime · Answer

And then $$\sqrt((20 - 85)^2 + (80 - 110)^2)$$?

mathmate · Answer

Since the route T-U-V and T-V-U both use U-V, we know they are equal.
So just compare which of T-U or T-V is shorter.
one of them is sqrt(5200), and the other is sqrt(5125), so make your choice.

anonymous · Answer

And what type of information do you need to find the shortest distance? and how can you use a diagram to help you?