the coordinates of a centroid of a triangle are(1,3) and two of its vertices are (-7,6) and (8,5) Find the - Maths - Coordinate Geometry

Question

the coordinates of a centroid of a triangle are(1,3) and two of its
vertices are (-7,6) and (8,5) Find the third vertex Also find the
the coordinates of the centroidof the triangle when the third
vertex is (2,4)

Varun.Rawat · Accepted Answer

We know that coordinates of the centroidx,y of a triangle having its vertices atx1,y1; x2,y2 and x3,y3 is,x = x1+x2+x33  ;  y = y1+y2+y33Now, we have 1,3 as the centroid of a ∆ whose two vertices are -7,6 and 8,5
Let the third vertex be a,b
Now, 1 = -7+8+a3 ⇒a = 23 = 6+5+b3⇒b = -2So, third vertex is 2,-2

When the third vertex is 2,4, then centroid of a ∆ is x = -7+8+23 = 33 = 1y = 6+5+43 = 153 = 5So,1,5 is the centroid of the ∆

the coordinates of a centroid of a triangle are(1,3) and two of its vertices are (-7,6) and (8,5).Find the third vertex.Also find the the coordinates of the centroidof the triangle when the third vertex is (2,4).