Question

Prove that the line through (−2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (4, 24).

Answer 1

⇒ The first line passes through points (−2, 6) and (4, 8),

Using the slope formula:

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

`m_1 = (8 - 6)/(4 - (-2))`

`m_1 = 2/6`

∴ `m_1 = 1/3`

⇒ The second line passes through points (8, 12) and (4, 24),

Using the slope formula:

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

`m_2 = (24 - 12)/(4 - 8)`

`m_2 = 12/-4`

∴ m₂ = −3

Let’s check if the product of the slopes is −1:

`m_1 xx m_2 = (1/3) xx (-3)`

m₁ × m₂ = −1

Since the product of the slopes is −1, the line through (−2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (4, 24).

Hence Proved.