Test Objectives
  • Demonstrate the ability to find the inclination of a line
  • Demonstrate the ability to find the angle between two lines
  • Demonstrate the ability to find the distance between a point and a line
Inclination of a Line Practice Test:

#1:

Instructions: Find the inclination of the line θ.

$$a)\hspace{.1em}x + 5y=20$$

$$b)\hspace{.1em}11x - 5y=-35$$


#2:

Instructions: Find the inclination of the line θ.

$$a)\hspace{.1em}x + y=3$$

$$b)\hspace{.1em}9x - y=-2$$


#3:

Instructions: Find the acute angle θ between the two lines.

$$a)\hspace{.1em}x - 3y=6, 2x + 3y=-24$$

$$b)\hspace{.1em}5x - y=-1, x - 2y=16$$


#4:

Instructions: Find the acute angle θ between the two lines.

$$a)\hspace{.1em}x + 3y=-24, 5x - 6y=6$$

$$b)\hspace{.1em}x - 4y=28, 15x + 4y=36$$


#5:

Instructions: Find the distance between the point and the line.

$$a)\hspace{.1em}x - 4y=17, (-3, 4)$$

$$b)\hspace{.1em}x - 2y=-2, (-1, 3)$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}θ ≈ 168.69°$$

$$b)\hspace{.1em}θ ≈ 65.56°$$


#2:

Solutions:

$$a)\hspace{.1em}θ=135°$$

$$b)\hspace{.1em}θ ≈ 83.66°$$


#3:

Solutions:

$$a)\hspace{.1em}θ ≈ 52.13°$$

$$b)\hspace{.1em}θ ≈ 52.13°$$


#4:

Solutions:

$$a)\hspace{.1em}θ ≈ 58.24°$$

$$b)\hspace{.1em}θ ≈ 89.10°$$


#5:

Solutions:

$$a)\hspace{.1em}d=\frac{36\sqrt{17}}{17}$$

$$b)\hspace{.1em}d=\sqrt{5}$$