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:
\[ \boxed{4.5} \text{ feet} \]
3 answers