Question

Show that the line segment joining (2, 3) and (5, −7) is parallel to the line segment joining (2, −1) and (−1, 9).

Answer 1

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂):

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

⇒ Let m₁ be the slope of the line segment joining A(2, 3) and B(5, −7):

`m_1 = (-7 - 3)/(5 - 2)`

`m_1 = (-10)/3`

∴ `m_1 = -10/3`

⇒ Let m₂ be the slope of the line segment joining C(2, −1) and D(−1, 9):

`m_2 = (9 - (-1))/(-1 - 2)`

`m_2 = (9 + 1)/-3`

`m_2 = 10/-3`

∴ `m_2 = -10/3`