Question

Three ballet dancers are positioned on stage. If Maddie is 2 feet straight behind Amanda and 4 feet directly left of Eli, how far is Amanda from Eli? If necessary, round to the nearest tenth.

Answer 1

To solve the problem, we can visualize the positions of the dancers on a coordinate plane for easier calculations.

Let's place Amanda at the coordinates (0, 0) on the plane.

Since Maddie is 2 feet straight behind Amanda, we assume “behind” means in the negative y-direction. Thus, Maddie's coordinates will be:

- Maddie: (0, -2)

Now, since Maddie is 4 feet directly left of Eli, we interpret "left" as negative x-direction. Therefore, if Maddie is to the left of Eli, we can set Eli's coordinates as follows (since Maddie is at (0, -2)):

- Maddie is 4 feet left of Eli:
- If Maddie's x-coordinate is 0, then Eli's x-coordinate must be:
\[
x_{Eli} = 0 + 4 = 4
\]
- Maddie's y-coordinate remains the same as for Maddie:
\[
y_{Eli} = -2 \quad (same \; y-coordinate \; as \; Maddie)
\]

Therefore, Eli's coordinates are:

- Eli: (4, -2)

Now, we can find the distance between Amanda (0, 0) and Eli (4, -2) using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the respective coordinates:

\[
d = \sqrt{(4 - 0)^2 + (-2 - 0)^2} = \sqrt{(4)^2 + (-2)^2} = \sqrt{16 + 4} = \sqrt{20} \approx 4.47
\]

Rounding to the nearest tenth, the distance from Amanda to Eli is approximately:

\[
\boxed{4.5} \text{ feet}
\]