Question

directions: determine if segments $\overline{ab}$ and $\overline{cd}$ are parallel, perpendicular, or neither.

1. $\overline{ab}$ formed by (-2, 13) and (0, 3)

$\overline{cd}$ formed by (-5, 0) and (10, 3)

1. $\overline{ab}$ formed by (3, 7) and (-6, 1)

$\overline{cd}$ formed by (-6, -5) and (0, -1)

1. $\overline{ab}$ formed by (-6, 2) and (-2, 4)

$\overline{cd}$ formed by (-1, 11) and (5, -7)

1. $\overline{ab}$ formed by (-3, 8) and (2, 3)

$\overline{cd}$ formed by (-4, 6) and (-8, 2)

1. $\overline{ab}$ formed by (-8, -1) and (-4, 2)

$\overline{cd}$ formed by (0, -3) and (12, 6)

1. $\overline{ab}$ formed by (6, 5) and (3, -1)

$\overline{cd}$ formed by (2, -5) and (-4, 7)

Explanation:

Step1: Find slope of $\overline{AB}$

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
For 1: $m_{AB} = \frac{3 - 13}{0 - (-2)} = \frac{-10}{2} = -5$
For 2: $m_{AB} = \frac{1 - 7}{-6 - 3} = \frac{-6}{-9} = \frac{2}{3}$
For 3: $m_{AB} = \frac{4 - 2}{-2 - (-6)} = \frac{2}{4} = \frac{1}{2}$
For 4: $m_{AB} = \frac{3 - 8}{2 - (-3)} = \frac{-5}{5} = -1$
For 5: $m_{AB} = \frac{2 - (-1)}{-4 - (-8)} = \frac{3}{4}$
For 6: $m_{AB} = \frac{-1 - 5}{3 - 6} = \frac{-6}{-3} = 2$

Step2: Find slope of $\overline{CD}$

For 1: $m_{CD} = \frac{3 - 0}{10 - (-5)} = \frac{3}{15} = \frac{1}{5}$
For 2: $m_{CD} = \frac{-1 - (-5)}{0 - (-6)} = \frac{4}{6} = \frac{2}{3}$
For 3: $m_{CD} = \frac{-7 - 11}{5 - (-1)} = \frac{-18}{6} = -3$
For 4: $m_{CD} = \frac{2 - 6}{-8 - (-4)} = \frac{-4}{-4} = 1$
For 5: $m_{CD} = \frac{6 - (-3)}{12 - 0} = \frac{9}{12} = \frac{3}{4}$
For 6: $m_{CD} = \frac{7 - (-5)}{-4 - 2} = \frac{12}{-6} = -2$

Step3: Compare slopes

Parallel: $m_{AB}=m_{CD}$; Perpendicular: $m_{AB} \times m_{CD} = -1$

1. $(-5) \times \frac{1}{5} = -1$ → perpendicular
2. $\frac{2}{3} = \frac{2}{3}$ → parallel
3. $\frac{1}{2}

eq -3$, $\frac{1}{2} \times (-3)
eq -1$ → neither

1. $(-1) \times 1 = -1$ → perpendicular
2. $\frac{3}{4} = \frac{3}{4}$ → parallel
3. $2

eq -2$, $2 \times (-2)
eq -1$ → neither

Answer:

1. Perpendicular
2. Parallel
3. Neither
4. Perpendicular
5. Parallel
6. Neither