Question

the equation of the right bisector of the line segments joining (1,-4) (3,5) is​

Answer 1

Answer:

4x + 18y - 17 = 0

Step-by-step explanation:

As the required line bisects the line joining (1, -4) and (3 , 5), it must be passing through the mid-point of line formed by (1 , -4) and (3 , 5).

Point from where the required line passes:

⇒ (1+3 /2 , -4+5 /2)

⇒ (2 , 1/2)               [Mid-point formula]

As the required line is perpendicular to the line joining (1. -4) and (3, 5),  then the product of their slopes must be -1.

  Slope of line joining (1, -4) and (3 , 5)

                      = (-4 - 5)/(1 - 3)

                      = 9/2

Therefore, the slope of the required line must be - 2/9. [being perpendicular]

Hence the equation of the required line is

⇒ y - y₍ = m(x - x₍)

⇒ y - 1/2 = (-2/9)(x - 2)

⇒ 18y - 9 = - 4x + 8

⇒ 4x + 18y - 17 = 0

Equation of the required line is 4x + 18y - 17 = 0

Answer 2

Answer:

★Point from where the required line passes:

$\sf \longrightarrow{(1 + \frac{3}{2} - 4 + \frac{5}{2}) }$

$\sf \longrightarrow{(2 \: \frac{1}{2} })$

★Slop of line joining (1,-4) (3,5)

$\sf \longrightarrow{ \frac{( - 4 - 5)}{(1 - 3)} }$

$\sf \longrightarrow{ \frac{9}{2} }$

★Hence the equation line is :

$\sf \longrightarrow{ y- y = m(x-x)}$

$\sf \longrightarrow{y - 1/2 = (-2/9)(x-2)}$

$\sf \longrightarrow{18y - 9 = -4x + 8}$

$\sf \longrightarrow{ 4x + 18y - 17 = 0}$

The equation of the right bisector if the line segments joining (1,-4) (3,5) is 4x + 18y - 17 = 0