To find the distance between Jacob and Sharon, we'll first determine their final positions based on the directions they walked, and then use the distance formula.
Jacob's position:
- Starts at the origin (0, 0).
- Walks 3 m north: This translates to the y-coordinate increasing by 3, so he is now at (0, 3).
- Walks 4 m west: This translates to the x-coordinate decreasing by 4, so he is now at (-4, 3).
So Jacob's coordinates are \((-4, 3)\).
Sharon's position:
- Starts at the origin (0, 0).
- Walks 5 m south: This translates to the y-coordinate decreasing by 5, so she is now at (0, -5).
- Walks 12 m east: This translates to the x-coordinate increasing by 12, so she is now at (12, -5).
So Sharon's coordinates are \((12, -5)\).
Distance Calculation: Now we can calculate the distance between Jacob and Sharon using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting in Jacob's coordinates \((-4, 3)\) as \((x_1, y_1)\) and Sharon's coordinates \((12, -5)\) as \((x_2, y_2)\): \[ d = \sqrt{(12 - (-4))^2 + (-5 - 3)^2} \] \[ = \sqrt{(12 + 4)^2 + (-8)^2} \] \[ = \sqrt{(16)^2 + (-8)^2} \] \[ = \sqrt{256 + 64} \] \[ = \sqrt{320} \] \[ = \sqrt{64 \times 5} \] \[ = 8\sqrt{5} \]
Now we can approximate \( \sqrt{5} \): \[ \sqrt{5} \approx 2.236 \] So, \[ 8\sqrt{5} \approx 8 \times 2.236 \approx 17.888 \]
Thus, we can round this to approximately 18 m.
Therefore, the distance between Jacob and Sharon is approximately 18 m.
The correct answer is D: 18 m.