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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m_1=\dfrac{9-15}{10-3}$

$m_1=\dfrac{-6}{7}$

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

$m_2=\dfrac{3-9}{9-2}$

$m_2=\dfrac{-6}{7}$

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