Question

if the two vertices of a triangle are (3, 6) , (-5, 2) and the centroid (5/3, 2/3) then the third vertex is​

Answer 1

Step-by-step explanation:

Given :-

The two vertices of a triangle are (3, 6) , (-5, 2) and the centroid (5/3, 2/3)

To find :-

Find the third vvertex of the triangle ?

Solution :-

Given two vertices of a triangle are (3, 6) , (-5, 2)

Let (x1, y1) = (3,6) => x1 = 3 and y1 = 6

Let (x2, y2) = (-5,2) => x2 = -5 and y2 = 2

Let the third vertex be (x3, y3)

We know that

The Centroid of the triangle formed by the vertices of a triangle is G(x,y)

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

On Substituting these values in the above formula then

=> G(x,y) = ( { 3-5+x3}/3 , { 6+2+y3}/3 )

=> G(x,y) = ( {-2+x3}/3 , {8+y3}/3 )

According to the given problem

The Centroid = (5/3, 2/3)

=> ( {-2+x3}/3 , {8+y3}/3 ) = (5/3, 2/3)

On comparing both sides then

=> {-2+x3}/3 = 5/3 and {8+y3}/3 = 2/3

=> -2+x3 = 5 and 8+y3 = 2

=> x3 = 5+2 and y3 = 2-8

=> x3 = 7 and y3 = -6

Therefore, (x3, y3) = (7,-6)

Answer:-

The third vertex of the given triangle is (7,-6)

Used formulae:-

The Centroid of the triangle formed by the vertices of a triangle is G(x,y)

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