Suppose that the sides passing through the vertex ( , ) of a triangle are bisected at right angles by the lines y^2-8 x y-9 x^2=0 . Then, the centoid of the triangle is

Step-by-step solution

y^2-8 x y-9 x^2=0y^2-9 x y+x y-9 x^2=0(y-9 x)(y+x)=0 The two given lines are y=9 x and y=-x Slope of line y=9 x is 9 and slope of line y=-x is -1 . Let A B and B C be the line perpendicular to y=9 x and y=-x respectively. Slope of A B= -1 9 and slope of line B C is 1. Equation of A B is y- = -1 9 (x- )9 y-9 =-x+ x+9 y- -9 =0M is Mid-point of the A B and y=9 x So, x+9(9 x)+ +9 82 x= +9 = +9 82 Coordinate of M is ( +9 82 , 9 +81 82 ) . M is Mid-point of A B , Let coordinate of A be h, k +9 82 = +h 2 and 9 +81 82 = +k