Question

the equation of the perpendicular bisector of the line segment joining (1,1)and(2,3) is _​

Answer 1

Answer:

y = - $\frac{1}{2}$ x + $\frac{11}{4}$

Step-by-step explanation:

Formula of a slope m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

Coordinate of midpoint are ( $\frac{x_{1} +x_{2} }{2}$ , $\frac{y_{1} +y_{2} }{2}$ )

If AB ⊥ CD, then $m_{AB}$ $m_{CD}$ = - 1

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

~~~~~~~~~~~~

(1, 1)

(2, 3)

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

Slope of perpendicular line is ( - $\frac{1}{2}$ )

Coordinates of midpoint: ( $\frac{1+2}{2}$ , $\frac{3+1}{2}$ ) = ( 1.5 , 2 )

y - 2 = - $\frac{1}{2}$ ( x - 1.5 )

y = - $\frac{1}{2}$ x + $\frac{11}{4}$