Question

For questions 18-20 determine if line segment AB and line segment CD are parallel, perpendicular or neither

Answer 1

Answer:

Part 18) Lines AB and CD are perpendicular

Part 19)  Lines AB and CD are parallel

Part 20) Lines AB and CD are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal each other (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Part 18) we have

$A(-4,3),B(2,-12),C(10,5).D(0,1)$

step 1

Find the slope AB

substitute the given values in the formula

$m=\frac{-12-3}{2+4}$

$m=-\frac{15}{6}$

step 2

Find the slope CD

substitute the given values in the formula

$m=\frac{1-5}{0-10}$

$m=\frac{4}{10}$

$m=\frac{2}{5}$

step 3

Compare the slopes

$-\frac{15}{6} \neq  \frac{2}{5}$ ----> the lines are not parallel

$-\frac{15}{6}*\frac{2}{5}=-1$ ----> the lines are perpendicular

Part 19) we have

$A(2,3),B(8,-15),C(-2,2).D(-5,11)$

step 1

Find the slope AB

substitute the given values in the formula

$m=\frac{-15-3}{8-2}$

$m=-\frac{18}{6}=-3$

step 2

Find the slope CD

substitute the given values in the formula

$m=\frac{11-2}{-5+2}$

$m=-\frac{9}{3}=-3$

step 3

Compare the slopes

$-3=-3$ ----> the lines are  parallel

Part 20) we have

$A(5,6),B(-1,6),C(-2,-7).D(-2,-4)$

step 1

Find the slope AB

substitute the given values in the formula

$m=\frac{6-6}{-1-5}$

$m=\frac{0}{-6}=0$  ----> is a horizontal line  parallel to the x-axis

step 2

Find the slope CD

substitute the given values in the formula

$m=\frac{-4+7}{-2+2}$

$m=\frac{3}{0}$  -----> is undefined (is a vertical line, parallel to the y-axis)

step 3

Compare the slopes

The lines are perpendicular (because the x-axis and the y-axis are perpendicular)