Question

Using slopes, prove that the points (−1, −2), (5, 1) and (11, 4) are collinear.

Answer 1

Given:

• A = (x₁, y₁) = (−1, −2)
• B = (x₂, y₂) = (5, 1)
• C = (x₃, y₃) = (11, 4)

The formula for slope (m) is:

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

⇒ Calculate the Slope of AB(m₁):

`m_1 = (1 - (-2))/(5 - (-1))`

`m_1 = (1 + 2)/(5 + 1)`

`m_1 = 3/6`

∴ `m_1 = 1/2`

⇒ Calculate the Slope of BC(m₂):

`m_2 = (4 - 1)/(11 - 5)`

`m_2 = 3/6`

∴ `m_2 = 1/2`

Since the Slope of AB = Slope of BC `(1/2 = 1/2)`, the line segments AB and BC are parallel. Because they share a common point B, the points A, B, and C lie on the same straight line.

Hence, the points (−1, −2), (5, 1) and (11, 4) are collinear.