Question

The centroid of a triangle is at the point (6,1) if two vertices of the triangle are (3,2) and (11,4) find the third vertex

Answer 1

Step-by-step explanation:

Cebtroid of a triangle =(6,1)

Coordinate of point A=(3,2)

Coordinate of point B=(11,4)

Coordinate of point C=

(3+11+x/3,2+4+y/3)=(6,1)

(14+x/3),(6+y/3)=(6,1)

x= 4 & y= -3

Answer 2

The third vertex is  (4,-3)

Explanation:

Given: centroid of a triangle=(6,1)

two vertices of the triangle=(3,2) and (11,4)

To find:  The third vertex

Solution:

Let the coordinates of the third vertex be (x, y).

Then,$\frac{x+3+11}{3}=6$  and $\frac{y+2+4}{3}=1$

$=x+14=18$ and $y +6=3$

$x=4$ and $y=-3$

Thus,the coordinates of the  third vertex are (4, -3).

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