1. Find equation of the perpendicular bisector of segment joining the points (2,-6) and (4,0)?
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By: anil on 05 May 2019 02.09 am
Let line $$l$$ perpendicularly bisects line joining A(2,-6) and B(4,0) at C, thus C is the mid point of AB. => Coordinates of C = $$(frac{2 + 4}{2} , frac{-6 + 0}{2})$$ = $$(frac{6}{2} , frac{-6}{2}) = (3,-3)$$ Now, slope of AB = $$frac{y_2 - y_1}{x_2 - x_1} = frac{(0 + 6)}{(4 - 2)}$$ = $$frac{6}{2} = 3$$ Let slope of line $$l = m$$ Product of slopes of two perpendicular lines = -1 => $$m imes 3 = -1$$ => $$m = frac{-1}{3}$$ Equation of a line passing through point $$(x_1,y_1)$$ and having slope $$m$$ is $$(y - y_1) = m(x - x_1)$$ $$ herefore$$ Equation of line $$l$$ => $$(y + 3) = frac{-1}{3}(x - 3)$$ => $$3y + 9 = -x + 3$$ => $$x + 3y = 3 - 9 = -6$$ => Ans - (B)
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