Geo2.17

From Exampleproblems

$A(10,4),B(-4,9),C(-2,-1)\,$ are the vertices of a triangle.Find the equations of i)AB. ii)Median through A. iii)Altitude through B. iv)Perpendicular bisector of side AB.

Equation of AB is

$y-4=\frac{9-4}{-4-10}(x-10)\,$

$-14y+56=5x-50\,$

$5x+14y-106=0\,$

Median of the traingle is

$\left(\frac{10-4-2}{3},\frac{4+9-1}{3}\right)\,$

$\frac{4}{3},4\,$

Now the equation of the line passing through A and median is

$y-4=\frac{4-4}{\frac{4}{3}-10}(x-10)\,$

$y-4=0\,$

The slope of AC is

$\frac{-1-4}{-2-10}=\frac{5}{12}\,$

Now the slope of the altitude is -12/5

Now the equation of altitude through B is

$y-9=\frac{-12}{5}(x+4)\,$

$5y-45=-12x-48\,$

$12x+5y+3=0\,$

Perpendicular bisector of side AB

The mid point of AB is $\frac{10-4}{2},\frac{4+9}{2}\,$

The slope of AB is -5/14,the slope of line perpendicular to this is 14/5.

hence the equation of perpendicular bisector is

$y-\frac{13}{2}=\frac{14}{5}(x-3)\,$

$10y-65=28x-84\,$

$28x-10y-19=0\,$

Main page:Geometry:Straight Lines-I

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