Question

1. on a maps coordinate grid, walt city is located at (1, 3) and koshville is located at (4, 9).

a) how long is a trains route as the train travels along a straight line from walt city to koshville?

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(1,3)\) and \((x_2,y_2)=(4,9)\).

Step2: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(x_2 - x_1=4 - 1 = 3\), \(y_2 - y_1=9 - 3 = 6\).
So \(d=\sqrt{3^2 + 6^2}=\sqrt{9 + 36}=\sqrt{45}\).
Simplify \(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx 6.71\) (rounded to two decimal places).

Answer:

The length of the train's route is \(3\sqrt{5}\approx6.71\) units.