Question

Line f passes through points (8, 7) and (3, 10). Line g passes through points (5, 7) and (10, 4). Are line f and line g parallel or perpendicular?

Answer 1

Answer: Parallel

Explanation:

First find slope.

Line f:
`(10-7)/(3-8) =-3/5`

Line g:
`(4-7)/(10-5)=-3/5`

Since the slopes are the same, the lines are parallel.

Answer 2

First we need to find the slope of each line

Slope of line f

(8 , 7) (3 , 10)

`slope = (y_(2)-y_(1) )/(x_(2)-x_(1))`

`slope = (10-7)/(3-8)`

`slope = (3)/(-5)`

`slope=-(3)/(5)`

Slope of line g

(5 , 7) (10 , 4)

`slope = (y_(2)-y_(1) )/(x_(2)-x_(1))`

`slope = (4-7)/(10-5)`

`slope = (-3)/(5)`

`slope=-(3)/(5)`

The two lines have the same slope therefore they are not perpendicular but instead parallel to each other.