Question

find the coordinates of the third vertex of a triangle whose two vertices and centroid are (0,0),(5,6), (0,3) respectievely

Answer 1

Answer:

The coordinates of the third vertex of a triangle are (-5,3).

Step-by-step explanation:

Two vertices of a triangle are (0,0),(5,6) and the centroid of the triangle is (0,3).

Let the coordinate of third vertex be (x,y).

The formula for centroid is

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

$(0,3)=(\frac{0+5+x}{3},\frac{0+6+y}{3})$

$(0,3)=(\frac{5+x}{3},\frac{6+y}{3})$

On comparing both the sides we get

$\frac{5+x}{3}=0$

$5+x=0$

$x=-5$

The value of x is -5.

$\frac{6+y}{3}=3$

$6+y=9$

$y=9-6=3$

The value of y is 3.

Therefore the coordinates of the third vertex of a triangle are (-5,3).