Chapter 13.3, Problem 5PSB

To determine

To find: The point of intersection of given two lines.

Answer to Problem 5PSB

Thepoint of intersection is $\left(2,7\right)$ .

Explanation of Solution

Given:

The line $\text{<mover accent="true"><mo>D</mo><mo>˙</mo></mover><mover accent="true"><mo>E</mo><mo>˙</mo></mover>}$ passes through the points are $\left(-5,0\right)\&\left(0,5\right)$ .

The line $\text{<mover accent="true"><mo>F</mo><mo>˙</mo></mover><mover accent="true"><mo>H</mo><mo>˙</mo></mover>}$ passes through the points are $\left(0,-3\right)\&\left(-1,0\right)$ .

Calculation:

Equation of line $\text{<mover accent="true"><mo>D</mo><mo>˙</mo></mover><mover accent="true"><mo>E</mo><mo>˙</mo></mover>}$ passes through the points are $\left(-5,0\right)\&\left(0,5\right)$ is given as:

  $\begin{array}{c}y=\frac{5-0}{0-\left(-5\right)}x-\left(-5\right)\\ y=x+5\left(1\right)\end{array}$

Equation of line $\text{<mover accent="true"><mo>F</mo><mo>˙</mo></mover><mover accent="true"><mo>H</mo><mo>˙</mo></mover>}$ passes through the points are $\left(0,-3\right)\&\left(-1,0\right)$ is given as:

  $\begin{array}{c}y+3=\frac{0+3}{-1-0}x-\left(0\right)\\ y=-3x-3\left(2\right)\end{array}$

The point of intersection is calculated as:

  $\begin{array}{c}x+5=-3x-3\left[\text{put equation}\left(1\right)=\text{equation}\left(2\right)\right]\\ x=2\\ y=2+5\left[\text{substitute }x=\text{2in equation}\left(1\right)\right]\\ y=7\end{array}$

Therefore the point of intersection is $\left(2,7\right)$ .