Question

F the coordinates of a and b be (1, 1) and (5, 7), then the equation of the perpendicular bisector of the line segment ab is

Answer 1

Answer: the equation of the perpendicular bisector of the line segment AB is $2x+3y=18$ .

Step-by-step explanation:

• Perpendicular bisector bisects a line segment into two equal halves and it is perpendicular to the original line.

Given : The coordinates of A and B are (1, 1) and (5, 7).

Then the mid point of segment AB = $(x,y)=(\dfrac{1+5}{2}, \dfrac{1+7}{2})=(3,4)$

The slope of line AB = $m=\dfrac{\text{change in y} }{\text{change in x}}=\dfrac{7-1}{5-1}=\dfrac{3}{2}$

The product of slopes of two lines is -1.

Let n be the slope of line perpendicular to AB , then

$n\times m=-1\\\Rightarrow\ n=\dfrac{-1}{m}=\dfrac{-2}{3}$

Equation of line passing through (3,4) and has slope $\dfrac{-2}{3}$ will be:

$(y-4)=\dfrac{-2}{3}(x-3)\\\\\Rightarrow\ 3y-12=-2x+6\\\\\Rightarrow\ 2x+3y=18$

Hence, the equation of the perpendicular bisector of the line segment AB is $2x+3y=18$ .

# Learn more :

the equation of perpendicular bisector of a line segment AB is x-y+5=0 if a=(1,-2) then AB is

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