Question

Answer the following question:

Find the equation of the line through A(−2, 3) and perpendicular to the line through S(1, 2) and T(2, 5)

Answer 1

Slope of ST = `(5 - 2)/(2 - 1) = 3/1` = 3

Since the required line is perpendicular to ST, the slope of the line is `-1/3` and it is passing through A(–2, 3).

∴ Equation of the line in slope point form is y − y₁ = m(x − x₁)

∴ The equation of the required line is

y – 3 = `-1/3(x + 2)`

∴ 3(y – 3) = –(x + 2)

∴ 3y – 9 = – x – 2

∴ x + 3y = 7