Question

the centroid of triangle ABC is (2,7).The points B, C lie on x, y axes respectively and A=(4,8).find B AND C

Answer 1

$\textbf{Answer :}$

Since, B and C lie on x and y axes respectively, let the coordinates of B and C are (x, 0) and (0, y) respectively.

Since, (2, 7) is the coordinates of the centroid of ABC triangle,

( (4 + x + 0)/3, (8 + 0 + y)/3 ) Ξ (2, 7)

i.e., ( (x + 4)/3, (y + 8)/3 ) Ξ (2, 7)

So, (x + 4)/3 = 2

or, x + 4 = 6

or, x = 2

and (y + 8)/3 = 7

or, y + 8 = 21

or, y = 13

Hence, the coordinates of B and C are (2, 0) and (0, 13) respectively.

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Answer 2

Value of B = (2,0) and C = (0,13).

To find :

Values for B and  C      

Given :

Centroid of triangle ABC is (2,7).

The point A is ( 4, 8 )

The points B and C lies on X and y axis.

Centroid formula :

                            Centroid = $(\frac{x_1+x_2+x_3}{3} ,\frac{y_1+y_2+y_3}{3} )$

Here,

         Centroid = ( 2, 7 )

         $(x_1, y_1)$ = ( 4, 8 )

         $(x_2, y_2)$ = ( x, 0 )

         $(x_3, y_3)$ = ( 0, y )

Applying the values in the centroid formula gives,

                                Centroid = $(\frac{x_1+x_2+x_3}{3} ,\frac{y_1+y_2+y_3}{3} )$

                                   ( 2, 7 )   =   $(\frac{4+x+0}{3} , \frac{8+0+y}{3} )$

                                  ( 2, 7 )   =  $(\frac{4+x}{3},\frac{8+y}{3})$

Now,

        $\frac{4+x}{3} = 2$            and             $\frac{8+y}{3} = 7$

       4 + $x$ = 6              and             8 + $y$ = 21

        $x$ = 6 - 4              and              $y$ = 21 - 8

             $x$ = 2              and                    $y$ = 13

Where,    

            $(x_2, y_2)$ = ( x, 0 )     and     $(x_3, y_3)$ = ( 0, y )

             $(x_2, y_2)$ = ( 2, 0 )    and      $(x_3, y_3)$ = ( 0, 13 )  

Thus, the points are A = ( 4, 8 ) , B = ( 2, 0 ) and C = ( 0 , 13 ).  

To learn more...

brainly.in/question/2479570