Question

26. Two vertices of a triangle are A (2, 1) and B (3, - 2). The third vertex C lies on
the line y = x + 9. If the centroid of A ABC lies on y-axis, find the coordinates
C and the centroid.​

Answer 1

Answer:

C( - 5 , 4 ) ; ( 0 , 1 )

Step-by-step explanation:

Assume that coordinates of point C( $x_{C}$ , $x_{C}$ + 9 )

The centroid is $\frac{2}{3}$ of the distance from vertex to the midpoint of the opposite side.

A(2, 1), B(3, - 2), C( $x_{C}$ , $x_{C}$ + 9 )

The coordinates of the centroid ( $\frac{5+x_{C} }{3}$ , $\frac{x_{C} +8}{3}$ )

$\frac{5+x_{C} }{3}$ = 0 ⇒ $x_{C}$ = - 5

$y_{C}$ = - 5 + 9 = 4

C( - 5 , 4 )

The coordinates of the centroid ( 0 , $\frac{-5+8}{3}$ ) = ( 0 , 1 )