Question

What is the equation of the perpendicular bisector of line AB?

A y=-5/12x+41/12
B y=-5/6x+41/12
C y=6/5x+12/5
D y=-6/5x+3

Answer 1

It should be B

Because the slope of AB is 6/5 and when you are finding it’s perpendicular bisector then the slope of that line should be the negative reciprocal, it should be -5/6.

Answer 2

The equation of the perpendicular bisector of line AB is option (B) $y=-\frac{5}{6} x+\frac{41}{12}$ is the correct answer.

What is equation of a line?

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

For the given situation,

The points on the plane are A(-2,0), B(3,6), C(8,0)

Let D be the midpoint of AB and DE be the line that is perpendicular bisector of line AB.

The formula of mid point of line (x₁,y₁) is A(-2,0) and (x₂,y₂) is B(3,6)

$D=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})$

The coordinate of D is

⇒ $D=(\frac{-2+3 }{2}, \frac{0+6}{2} )$

⇒ $D=(\frac{1 }{2}, \frac{6}{2} )$

⇒ $D=(\frac{1 }{2}, 3 )$

The formula of slope of AB is

Slope of AB = $\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

⇒ $m_{1} =\frac{6-0 }{3-(-2)}$

⇒ $m_{1} =\frac{6 }{3+2}$

⇒ $m_{1} =\frac{6}{5}$

The DE is perpendicular to AB, so the slope of DE is negative reciprocal of AB.

Then the slope of DE, $m_{2} =-\frac{5}{6}$

The formula of the equation of line in slope intercept form is

$y-y_{1}=m(x-x_{1} )$

Now, equation of line DE is

⇒ $y-3=-\frac{5}{6} (x-\frac{1}{2} )$

⇒ $y-3=-\frac{5}{6} x+\frac{5}{12}$

⇒ $y=-\frac{5}{6} x+\frac{5}{12}+3$

⇒ $y=-\frac{5}{6} x+\frac{5+36}{12}$

⇒ $y=-\frac{5}{6} x+\frac{41}{12}$

Hence we can conclude that the equation of the perpendicular bisector of line AB is option (B) $y=-\frac{5}{6} x+\frac{41}{12}$ is the correct answer.

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