Question

Line m passes through points (3, 15) and (10,9). Line n passes through points (2,9) and (9,3). Are line m and line n parallel perpendicular?

Answer 1

Given:

Line m passes through points (3, 15) and (10,9).

Line n passes through points (2,9) and (9,3).

To find:

Whether the line m and line n are parallel or perpendicular?

Solution:

Slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Line m passes through points (3, 15) and (10,9). Using the slope formula, the slope of line m is

`m_1=(9-15)/(10-3)`

`m_1=(-6)/(7)`

Line n passes through points (2, 9) and (9,3). Using the slope formula, the slope of line m is

`m_2=(3-9)/(9-2)`

`m_2=(-6)/(7)`

Since
`m_1=m_2`, therefore, the lines m and n are parallel because the slope of parallel lines are equal.