Question

Line g passes through points (5, 9) and (3, 2). Line h passes through points (9, 10) and (2, 12). Are line g and line h parallel or perpendicular?

Answer 1

For this case we find the slopes of each of the lines:

The g line passes through the following points:

`(x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}) :( 5,9)`

So, the slope is:

`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {9-2} {5-3} = \frac {7} {2}`

Line h passes through the following points:

`(x_ {1}, y_ {1}) :( 9,10)\\(x_ {2}, y_ {2}) :( 2,12)`

So, the slope is:

`m = \frac {y_ {2} -y_ {1}}{x_ {2} -x_ {1}} = \frac {12-10} {2-9} = \frac {2} {- 7} = - \frac {2} {7}`

By definition, if two lines are parallel then their slopes are equal. If the lines are perpendicular then the product of their slopes is -1.

It is observed that lines g and h are not parallel. We verify if they are perpendicular:

`\frac {7} {2} * - \frac {2} {7} = \frac {-14} {14} = - 1`

Thus, the lines are perpendicular.

Answer:

The lines are perpendicular.