Question

find the third vertex of triangle ABC if two of its vertices (-3 ,1 )and (0 ,- 2 ) and centroid is at origin

Answer 1

Answer:

The third vertex of triangle is :(3,1)

Step-by-step explanation:

Let the third vertex be (x,y)  and other two vertices are (-3,1) and (0,-2)

Coordinates of  centroid  of triangle  =(0,0)

∴ [-3+0+x/3 , 1-2+y/3] = (0,0)

-3+x/3 = 0

x-3=0

x=3

and 1-2+y/3 =0

y-1/3=0

y-1=0

y=1

∴ x=3 and y=1

Answer 2

we know, if three vertices of triangle are $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$
then, centroid of triangle is given by,
$\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)$

here given, two vertices of triangle ABC are (-3, 1) and (0, -2) and question want to find third vertex of triangle when centroid of triangle lies at origin.

assume third vertex is $(x,y)$

so, $(0,0)=\left(\frac{-3+0+x}{3},\frac{1-2+y}{3}\right)$

(x - 3)/3 = 0 => x = 3

and (-1 + y)/3 = 0 => y = 1

hence, third vertex is (3,1)