Find the equation of a line which is perpendicular to the line $3 x + 2 y - 8 = 0$ and passes through the midpoint of the line joining the points $(6, 4)$ and $(4, - 2)$

Open in App

Solution

Given points $(6, 4)$ and $(4, - 2)$
Mid point of line joining given points is $(5, 1)$ $
Equation of line perpendicular to line $3 x + 2 y - 8 = 0$ is
$2 x - 3 y - λ = 0$ ---(1)
On passing above equation through $(5, 1)$
$10 - 3 - λ = 0$
$λ = 7$
From eq (1)
$2 x - 3 y - 7 = 0$

Suggest Corrections

Similar questions

Q. Find the equation of the straight line which passes through the point of intersection of the straight lines x + y = 8 and 3x - 2y + 1 = 0 and is parallel to the straight line joining the points (3, 4) and (5, 6).

Find the equation of the straight line perpendicular to $5 x - 2 y = 8$ and which passes through the mid-point of the line segement joining $(2, 3)$ and $(4, 5)$ .

Q. Find the equation of the straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0

Q. Find the equation of the line passing through the point

(2, 3)

and perpendicular to the line

3 x + 2 y - 1 = 0

Q. Find the equation to the straight line which passes through point of intersection of line

2 x + y + 1 = 0

3 x - y + 4 = 0

and is parallel to line

3 x - 2 y = 0

Join BYJU'S Learning Program

Find the equation of a line which is perpendicular to the line 3x+2y−8=0 and passes through the midpoint of the line joining the points (6,4) and (4,−2)

Given points (6,4) and (4,−2)Mid point of line joining given points is (5,1)$Equation of line perpendicular to line 3x+2y−8=0 is 2x−3y−λ=0---(1)On passing above equation through (5,1)10−3−λ=0λ=7From eq (1)2x−3y−7=0

Find the equation of a line which is perpendicular to the line $3 x + 2 y - 8 = 0$ and passes through the midpoint of the line joining the points $(6, 4)$ and $(4, - 2)$

Given points $(6, 4)$ and $(4, - 2)$
Mid point of line joining given points is $(5, 1)$ $
Equation of line perpendicular to line $3 x + 2 y - 8 = 0$ is
$2 x - 3 y - λ = 0$ ---(1)
On passing above equation through $(5, 1)$
$10 - 3 - λ = 0$
$λ = 7$
From eq (1)
$2 x - 3 y - 7 = 0$