Question

Find the equation of the line that is the perpendicular bisector of AB

Answer 1

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m of AB

m = $\frac{rise}{run}$ = $\frac{3}{2}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{2} }$ = - $\frac{2}{3}$

To find the midpoint of AB use the midpoint formula

M = [ $\frac{1}{2}$(x₁ + x₂ ), $\frac{1}{2}$ (y₁ + y₂ ) ]

with (x₁, y₁ ) = )0, 0) and (x₂, y₂ ) = (2, 3), thus

M = [ $\frac{1}{2}$(0 + 2), $\frac{1}{2}$(0 + 3 )] = (1, $\frac{3}{2}$ )

Partial equation of perpendicular bisector is

y = - $\frac{2}{3}$ x + c

To find c substitute (1, $\frac{3}{2}$ ) into the partial equation

$\frac{3}{2}$ = - $\frac{2}{3}$ + c ⇒ c = $\frac{3}{2}$ + $\frac{2}{3}$ = $\frac{13}{6}$

y = - $\frac{2}{3}$ x + $\frac{13}{6}$ → D