Question

find the centroid of the triangle whose equations of the sides are 4x-y-19=0,x-y-4=0,x+2y+11=0.​

Answer 1

Answer:

The equations are 4x-y-19=0, x-y-4=0 and x+2y+11=0

Taking the equations in pairs and solving each pair, we get the coordinates of the three vertices of the triangle as (5,1),(-1,-5) & (3,-7)

Here,x1=5,y1=1

x2= -1,ye= -5

x3=3,y3= -7

centroid of triangle={(x1+x2+x3)/3,(y1+y2+y3)/3}

={(5-1+3)/3,(1-5-7)/3}

=(7/3,-11/3)________(ans)