Chapter 7.7, Problem 10CFU

To determine

To find: the distance between Juwan’s position and the road.

Explanation of Solution

Given information:

Juwan moves to 2000 feet east from the road and stops.

The units are hundreds of feet and the positive y- axis of the coordinate system points north.

The equation of road is shown below.

  $5x-3y=0$

Calculation:

Since the units are hundreds of feet, so the point coordinate $\left(x_1,y_1\right)$ for the distance of 2000 feet due east will be $\left(20,0\right)$ .

The road equation is in the standard form where $A=5,B=-3$ and $C=0$ .

The distance from a point to a line $\left(d\right)$ will be evaluated as shown below.

  $\begin{array}{c}d=\left|\frac{\left|A{x}_1+B{y}_1+C\right|}{\pm \sqrt{A^2+B^2}}\right|\left[\text{Take absolute value of }d\text{ as distance cannot be negative}\right]\\ =\left|\frac{\left|5\left(20\right)+\left(-3\right)\left(0\right)+0\right|}{\pm \sqrt{{\left(5\right)}^2+{\left(-3\right)}^2}}\right|\left[\text{Put the values of }A,B,C,x_1\text{ and }{y}_1\right]\\ =\left|\frac{\left|100\right|}{\pm \sqrt{25+9}}\right|\\ =\frac{100}{\sqrt{34}}\\ =17.15\\ =1715\text{ feet }\left[\because \text{Units are 100 of feet}\right]\end{array}$

Thus the distance from the road to the point of location of Juwan is 1715 feet.