Three ballet dancers are positioned on stage. Leo is 1 meter straight behind Eve and 2 meters

Question

directly left of Abby. When the music begins, Leo twirls to Abby's position, then leaps to Eve's
position, and finally walks back to his original position. How far did Leo travel? If necessary,
round to the nearest tenth.

Answer 1

To solve the problem, we need to find the distances Leo traveled during his twirl, leap, and walk.

First, let's find the distance between Leo and Abby before the twirl. Using the Pythagorean theorem, we have:

distance between Leo and Abby = √(1^2 + 2^2) = √5

Next, let's find the distance between Abby and Eve. Since we know that Leo is straight behind Eve, we can use the Pythagorean theorem again to find the distance between Abby and Eve:

distance between Abby and Eve = √(2^2 + 1^2) = √5

Now we can find the distance Leo traveled during his twirl. He moved from his original position to Abby's position, which we know is √5 meters away.

During his leap, Leo moved from Abby's position to Eve's position. Since we know the distance between Abby and Eve is also √5, we can use the Pythagorean theorem one more time to find the distance Leo traveled during his leap:

distance traveled during leap = √[(√5)^2 + (√5)^2] = √20 = 2√5

Finally, during his walk, Leo traveled 1 meter back to his original position.

Adding up the three distances, we get:

total distance traveled = √5 + 2√5 + 1 ≈ 4.2 meters

So Leo traveled approximately 4.2 meters during his twirl, leap, and walk.