Question

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)

Answer 1

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.

Answer 2

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