Find the equation of the line through A(-2, 3) and perpendicular to th

1.	Find the equation of the line through A(-2, 3) and perpendicular to the line through S(1, 2) and T(2, 5).
Answer» Slope of ST = 5-2/ 2-1 = 3 Since the required line is perpendicular to ST, slope of required line = -1/3 and lines passes through A(-2,3) Equation of the line in slope point form is y₁ – y = 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

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

Answer»

Slope of ST = 5-2/ 2-1 = 3

Since the required line is perpendicular to ST, slope of required line = -1/3 and lines passes through A(-2,3)

Equation of the line in slope point form is y₁ – y = 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