Chapter 11.1, Problem 34IP

a.

To determine

To graph: The three lines on same coordinate plane.

Explanation of Solution

Given: Line f passes through points at $\left(0,2\right)\text{ and }\left(2,3\right)$ . Line g passes through points at $\left(0,-3\right)\text{ and }\left(2,-2\right)$ . Line h passes through points at $\left(1,0\right)\text{ and }\left(2,-2\right)$ .

Plot the points and draw the graph of all three lines.

  

b.

To determine

To write: The angles formed by three lines.

Answer to Problem 34IP

Line f and g are making angle $0^{\circ }$

Line f and h are making angle ${90}^{\circ }$

Line g and h are making angle ${90}^{\circ }$

Explanation of Solution

Given: Line f passes through points at $\left(0,2\right)\text{ and }\left(2,3\right)$ . Line g passes through points at $\left(0,-3\right)\text{ and }\left(2,-2\right)$ . Line h passes through points at $\left(1,0\right)\text{ and }\left(2,-2\right)$ .

Plot the points and draw the graph of all three lines.

  

According to graph.

Line f and g are parallel so making angle $0^{\circ }$

Line f and h are perpendicular so making angle ${90}^{\circ }$

Line g and h are perpendicular so making angle ${90}^{\circ }$

c.

To determine

To write: The angles formed by three lines.

Answer to Problem 34IP

Line f and g are making angle $0^{\circ }$

Line f and h are making angle ${90}^{\circ }$

Line g and h are making angle ${90}^{\circ }$

Explanation of Solution

Given: Line f passes through points at $\left(0,2\right)\text{ and }\left(2,3\right)$ . Line g passes through points at $\left(0,-3\right)\text{ and }\left(2,-2\right)$ . Line h passes through points at $\left(1,0\right)\text{ and }\left(2,-2\right)$ .

Plot the points and draw the graph of all three lines.

  

According to graph.

Line f and g are parallel so making angle $0^{\circ }$

The equation of line $f:y=\frac{1}{2}x+2\text{ and Equation of line }g:y=\frac{1}{2}x-3$

Both are in slope intercept form.

Slope of line $f\text{ is }\frac{1}{2}\text{ and }g\text{ is }\frac{1}{2}.$

Hence, the slope of parallel lines are equal.