Question

Determine whether PQ and UV are parallel,

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The slope of a line (m) is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

Two lines are parallel if they have the same slope and perpendicular if the product of their slope is -1.

1)

$Slope\ of\ PQ=\frac{1-(-2)}{9-(-3)}=\frac{1}{4} \\\\Slope\ of\ UV=\frac{-2-6}{5-3}=-4$

Since the product of their slope is -1, they are perpendicular

2)

$Slope\ of\ PQ=\frac{1-7}{2-(-10)}=-\frac{1}{2} \\\\Slope\ of\ UV=\frac{1-0}{6-4}=\frac{1}{2}$

Since the slope is not the same or product of their slope is not -1, they are neither parallel or perpendicular

3)

$Slope\ of\ PQ=\frac{8-1}{9-1}=\frac{7}{8} \\\\Slope\ of\ UV=\frac{8-1}{2-(-6)}=\frac{7}{8}$

Since the slopes are the same, they are parallel

4)

$Slope\ of\ PQ=\frac{3-0}{9-(-4)}=\frac{3}{4} \\\\Slope\ of\ UV=\frac{6-(-3)}{8-(-4)}=\frac{3}{4}$

Since the slopes are the same, they are parallel

5)

$Slope\ of\ PQ=\frac{1-2}{0-(-9)}=-\frac{1}{9} \\\\Slope\ of\ UV=\frac{-1-8}{-2-(-1)}=9$

Since the product of their slope is -1, they are perpendicular

Answer 2

Answer:

9

Step-by-step explanation: