Question

4. If the centroid of a triangle is at (1, 3) and two of its vertices are (-7, 6) and (8, 5) then
find the third vertex of the triangle .

Answer 1

Hi ,

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#Centroid of the triangle :

The centroid of the triangle formed

by the points A( x1 , y1 ) , B( x2 , y2 ),

C( x3 , y3 ) is

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

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Let the third vertex = ( x , y )

Centroid of the triangle whose

vertices are ( -7 , 6 ) ,( 8 , 5 ) and (x ,y)

is ( 1 , 3 )

( -7 + 8 + x /3 , 6 + 5 + y /3 ) = ( 1 , 3 )

( 1 + x/3 , 11 + y/3 ) = ( 1 , 3 )

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If ( a , b ) = ( c , d ) then

a = c , b = d

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(1 + x) /3 = 1

1 + x = 3

x = 3 - 1

x = 2 ,

And

( 11 + y )/3 = 3

11 + y = 9

y = 9 - 11

y = - 2

Therefore ,

Third vertex = ( x , y ) = ( 2 , - 2 )

I hope this helps you.

: )

Answer 2

Answer:

The centroid of the triangle formed

by the points A( x1 , y1 ) , B( x2 , y2 ),

C( x3 , y3 ) is

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

Let the third vertex = ( x , y )

Centroid of the triangle whose

vertices are ( -7 , 6 ) ,( 8 , 5 ) and (x ,y)

is ( 1 , 3 )

( -7 + 8 + x /3 , 6 + 5 + y /3 ) = ( 1 , 3 )

( 1 + x/3 , 11 + y/3 ) = ( 1 , 3 )

If ( a , b ) = ( c , d ) then

a = c , b = d

 

(1 + x) /3 = 1

1 + x = 3

x = 3 - 1

x = 2 ,

And

( 11 + y )/3 = 3

11 + y = 9

y = 9 - 11

y = - 2

Therefore ,

Third vertex = ( x , y ) = ( 2 , - 2 )

Step-by-step explanation: