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

Assume each grid - square represents 10 units. Let the coordinates of platform B be \((- 30,30)\) and of platform C be \((10, - 10)\).

Step2: Apply distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-30,y_1 = 30,x_2 = 10,y_2=-10\).
\[

$$\begin{align*} d&=\sqrt{(10-(-30))^2+((-10)-30)^2}\\ &=\sqrt{(10 + 30)^2+(-10 - 30)^2}\\ &=\sqrt{(40)^2+(-40)^2}\\ &=\sqrt{1600 + 1600}\\ &=\sqrt{3200}\\ &=\sqrt{1600\times2}\\ & = 40\sqrt{2}\approx40\times1.414 = 56.6 \end{align*}$$

\]

Answer:

56.6