Question

The co-ordinates of the centroid of a triangle ABC are (-1,-2) what are the co-ordinates of vertex C, if co-ordinates of A and B are (6,-4) and (-2,2) respectively?

A) (-7,-4) B) (7,4) C) (7,-4) D) (-7,4)

Answer 1

Answer:

$(-7, -4)$

Step-by-step explanation:

We know that the coordinates of the centroid of a triangle are -

$\bigg (\dfrac{A_x+B_x+C_x}{3}, \dfrac{A_y+B_y+C_y}{3} \bigg)$       ..............(1)

where A, B, C are the vertices of a Triangle

Given, centroid = $(-1, -2)$       ...............(2)

$A(6, -4)$        ..................(3)

$B(-2, 2)$        ..................(4)

From (1), (2) we get -

$\dfrac{A_x+B_x+C_x}{3} = -1$

$=> \dfrac{6-2+C_x}{3} = -1$           (from (3) and (4))

$=> 4+C_x=-3$

$=> C_x=-7$

Similarly,

$\dfrac{A_y+B_y+C_y}{3} =-2$

$=> \dfrac{-4+2+C_y}{3}=-2$        (from (3) and (4))

$=> -2+C_y=-6$

$=> C_y=-4$

Therefore coordinates of point C are $(-7, -4)$