find the coordinates of the incentre and centroid of the triangle whose sides have the equation 3x -4y=0, 12y+5x=0, y-15=0.

also please tell me what is incentre, circumcentre, orthocentre and centroid in a triangle

Centroid of Triangle-

Incentre of Triangle-

Circum Centre of Triangle-

Orthocentre of Triangle-

We have to find the co-ordinates of the centroid and the incentre of the triangle which is formed by the 3 lines whose equations are-

*3x-4y=0 *

*12y+5x=0*

*y-15=0*

Solve the 3 linear equation taking 2 at a time to get the co-ordinates of the vertices of the triangle as-

A(0,0) B(20,15) C(-36,15)

Now use distance formula to calculate the sides of the triangle as,

Thus centroid,

co-ordinates of incentre are-

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