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:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Line m passes through points (3, 15) and (10,9). Using the slope formula, the slope of line m is
[tex]m_1=\dfrac{9-15}{10-3}[/tex]
[tex]m_1=\dfrac{-6}{7}[/tex]
Line n passes through points (2, 9) and (9,3). Using the slope formula, the slope of line m is
[tex]m_2=\dfrac{3-9}{9-2}[/tex]
[tex]m_2=\dfrac{-6}{7}[/tex]
Since [tex]m_1=m_2[/tex], therefore, the lines m and n are parallel because the slope of parallel lines are equal.
