Question

Find the equation of a line passing through (6, −2) and perpendicular to the line joining the points (6, 7) and (2, −3)

Answer 1

Let the vertices A(6, 7), B(2, −3), D(6, −2)

Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`

Slope of AB = `(-3 - 7)/(2 - 6) = (-10)/(-4) = 5/2`

lope of its perpendicular (CD) = `-2/5`

Equation of the line CD is y – y₁ = m(x – x₁)

y + 2 = `-2/5(x - 6)`

5(y + 2) = – 2(x – 6)

5y + 10 = – 2x + 12

2x + 5y + 10 – 12 = 0

2x + 5y – 2 = 0

The equation of the line is 2x + 5y – 2 = 0