Browse Questions

# Find the equation of the right bisector of the line segment joining the points (3,4) and (-1,2)

$\begin{array}{1 1}(A)\;2x+y=5 \\(B)\; 2x-y=5 \\(C)\; 2y-x=5 \\(D)\;2y+x=5 \end{array}$

Toolbox:
• The coordinates of the midpoint of a line passing through $(x_1, y_1)$ and $(x_2, y_2)$ is $\bigg( \large\frac{x_1+x_2}{2}$$, \large\frac{y_1+y_2}{2} \bigg) • Slope of the line is \bigg( \large\frac{y_2-y_1}{x_2-x_1} \bigg) • If two lines are perpendicular then the product of the slopes is -1. The end points of the line segment are A(3,4) and B(-1,2) Hence the midpoint of the line AB is \bigg( \large\frac{3-1}{2}$$, \large\frac{4+2}{2} \bigg)$
$\qquad = (1,3)$
Now the slope of the line is
$m_1 = \large\frac{2-4}{-1-3}$$= \large\frac{-2}{-4}$$ = \large\frac{1}{2}$
Hence the slope of the perpendicular will be