Question

three ballet dancers are positioned on stage. jenna is 3.1 feet straight behind christine and 2.5 feet directly left of dillon. when the music begins, jenna twirls to dillons position, then leaps to christines position, and finally walks back to her original position. how far did jenna travel? if necessary, round to the nearest tenth.

feet

Explanation:

Step1: Find the distance from Jenna to Dillon

Use the Pythagorean theorem. Let \(a = 2.5\) and \(b=3.1\). The distance \(d_{JD}=\sqrt{a^{2}+b^{2}}\).

$$d_{JD}=\sqrt{2.5^{2}+3.1^{2}}=\sqrt{6.25 + 9.61}=\sqrt{15.86}\approx3.98$$

Step2: Calculate the total distance Jenna traveled

Jenna's path is \(JD + DC+CJ\). Since \(DC = 3.1\) (Jenna to Christine) and \(CJ = 2.5\) (Christine to Jenna's original position, and \(JD\approx3.98\).
Total distance \(D=3.98+3.1 + 2.5\)

$$D=9.58\approx9.6$$

Answer:

\(9.6\)