Question

Find the equation of the line passing through the point (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).

Answer 1

Slope of the line through the points (2, 5) and (-3, 6)

\(\frac{y_2 - y_1}{x_2 -x_1} = \frac{6-(5)}{-3-2} = -\frac{1}{5}\)

Then the slope of the required line is 5. Hence the equation is y – y₁ = m(x – x₁)

⇒ y – 5 = 5(x – (-3)

⇒ y – 5 = 5x + 15 

⇒ 5x – y + 20 = 0.