Question

on a zip - line course, you are harnessed to a cable that travels through the treetops. you start at platform a and zip to each of the other platforms. how far do you travel from platform b to platform c? the distance from platform b to platform c is approximately meters. (round to the nearest tenth of a meter as needed.)

Explanation:

Step1: Identify coordinates

Let the coordinates of platform B be $(x_1,y_1)$ and of platform C be $(x_2,y_2)$. Assume B is at $(- 20,0)$ and C is at $(10,-10)$ (by observing the grid - each square represents a certain unit, assume 10 units per square).

Step2: Apply 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 $x_1=-20,y_1 = 0,x_2 = 10,y_2=-10$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(10-(-20))^2+(-10 - 0)^2}\\ &=\sqrt{(10 + 20)^2+(-10)^2}\\ &=\sqrt{30^2+(-10)^2}\\ &=\sqrt{900 + 100}\\ &=\sqrt{1000}\\ &\approx32 \end{align*}$$

\]

Answer:

32