Question

The line passing through (−4, −2) and (2, −3) is perpendicular to the line passing through (a, 5) and (2, −1). Find a.

Answer 1

Slope of the line passing through (−4, −2) and (2, −3) is m₁

`m_1 = (-3 + 2)/(2 + 4) = (-1)/6`

Slope of the line passing through (a, 5) and (2, −1) is m₂

`m_2 = (-1 - 5)/(2 - a) = (-6)/(2 - a)`

Since, the lines are perpendicular 

`m_1 = (-1)/m_2`

∴ `(-1)/6 = (-1)/((-6)/(2 - a))`

∴ `(-1)/6 = (2 - a)/6`

∴ (2 – a) = –1

∴ a = 3