Question

1. deriving the pythagorean theorem to find the length of the cable car route

discuss & write: use the points (-6404,8570) and (80,9800) to find the vertical and horizontal distances between the two towns. show your work.

Explanation:

Step1: Calculate horizontal distance

The horizontal distance $d_x$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $|x_2 - x_1|$. Here, $x_1=-6404$, $x_2 = 80$. So $d_x=|80-(-6404)|=|80 + 6404|=6484$.

Step2: Calculate vertical distance

The vertical distance $d_y$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $|y_2 - y_1|$. Here, $y_1 = 8570$, $y_2=9800$. So $d_y=|9800 - 8570|=1230$.

Answer:

Horizontal distance: 6484 ft, Vertical distance: 1230 ft