Question

1f the centroid of the triangle is (3, 4) the vertices of triangle are A(2,3) B(6,5) find the 3rd vertex.​

Answer 1

Step-by-step explanation:

Given:-

the centroid of the triangle is (3, 4) the vertices of triangle are A(2,3) B(6,5)

To find:-

If the centroid of the triangle is (3, 4) the vertices of triangle are A(2,3) B(6,5) find the 3rd vertex.

Solution:-

Given vertices of the triangle are A(2,3) B(6,5)

Let (x1, y1)=(2,3)=>x1=2 ; y1=3

Let (x2, y2)=(6,5)=>x2= 6 ; y2=5

Let the third vertex be (x3, y3)

Centroid of the triangle whose vertices are

(x1, y1), (x2, y2) and (x3, y3) is denoted by G(x,y) and defined by [(x1+x2+x3)/3 , (y1+y2+y3)/3]

now

G(x,y)=[(2+6+x3)/3 ,(3+5+y3)/3]

=>G(x,y)=[(8+x3)/3 , (8+y3)/3]

According to the given problem

The centroid of the triangle = (3,4)

=> [(8+x3)/3 , (8+y3)/3] = (3,4)

=>(8+x3)/3=3 and (8+y3)/3=4

=>8+x3=3×3 and 8+y3=4×3

=>8+x3=9 and 8+y3=12

=>x3=9-8 and y3=12-8

=>x3=1 and y3=4

therefore,(x3,y3)=(1,4)

Answer:-

The third vertex of the given triangle is (1,4)

Used formula:-

• Centroid of the triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) is denoted by G(x,y) and defined by

[(x1+x2+x3)/3 , (y1+y2+y3)/3]