Question

Three people are sitting on a bus. Alexandra is seated 4 meters directly behind Martin and 3 meters directly left of Gary. How far is Martin from Gary?

meters

Answer 1

To determine the distance between Martin and Gary, let's visualize the seating arrangement based on the given information.

1. **Positioning of Alexandra**:
- Alexandra is seated 4 meters directly behind Martin. This means if we consider Martin's position as a reference point (let's say at coordinates (0, 0)), Alexandra is at (0, -4), since she is behind him.

2. **Positioning of Gary**:
- Alexandra is also seated 3 meters directly left of Gary. If we consider Alexandra's position as (x, y) = (0, -4), and since she is to the left of Gary, Gary's position would be to the right of her. Therefore, Gary would be at (3, -4).

3. **Calculating the Distance from Martin to Gary**:
Martin is at (0, 0), and Gary is at (3, -4). We can use the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Where \((x_1, y_1)\) are the coordinates of Martin and \((x_2, y_2)\) are the coordinates of Gary.

Plugging in the values:

\[
\text{Distance} = \sqrt{(3 - 0)^2 + (-4 - 0)^2}
\]
\[
= \sqrt{3^2 + (-4)^2}
\]
\[
= \sqrt{9 + 16}
\]
\[
= \sqrt{25}
\]
\[
= 5 \text{ meters}
\]

Thus, the distance from Martin to Gary is **5 meters**.