90.7k views
1 vote
Determine if the lines that pass through the given points are parallel, perpendicular or neither.

Line A: (-8, 8) and (-5, 10) Line B: (-7, 12) and (-5. 15)

User Anand S
by
7.3k points

2 Answers

4 votes

Answer:

Lines A and B are neither parallel nor perpendicular lines.

Explanation:

For two lines,

if their slopes are equal then the lines are parallel; and

if the slope of one line is the negative reciprocal of the slope of the other line, then the two lines are equal.

Finding the slopes of line A and B:


mA= ((10-8))/((-5-(-8))) = (2)/(3)


mB = (15-12)/(-5-(-7)) = (3)/(2)


(2)/(3)
\\eq (3)/(2) and neither they are the negative reciprocal of each other so the lines A and B are neither parallel nor perpendicular lines.

User Ken Geis
by
7.4k points
6 votes

The equation of the line passing through the points
(x_1,y_1) and
(x_2,y_2) is


(x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1).

Then

1) the equation of line A is


(x-(-8))/(-5-(-8))=(y-8)/(10-8),\\ \\(x+8)/(3)=(y-8)/(2),\\ \\2(x+8)=3(y-8),\\ \\2x+16=3y-24,\\ \\2x-3y+40=0.

2) the equation of line B is


(x-(-7))/(-5-(-7))=(y-12)/(15-12),\\ \\(x+7)/(2)=(y-12)/(3),\\ \\3(x+7)=2(y-12),\\ \\3x+21=2y-24,\\ \\3x-2y+45=0.

Since
2\cdot 3+(-3)\cdot (-2)=12\\eq 0, then lines are not perpendicular.

Since
(2)/(3)\\eq (-3)/(-2), then lines are not parallel.

Answer: neither parallel, nor perpendicular


User Wenjie
by
8.6k points

No related questions found