Question

two vertices of a triangle have coordinates - 8, 7 and 9, 4 if the centroid of the triangle is at the origin what are the coordinates of the third vertex​

Answer 1

Answer :-

$\bf\huge\boxed{-17,-11}$

Explanation :-

Given :

• First vertex (A) = (8 , 7)

• Second vertex (B) = (9 , 4)

We know that if the centroid is at origin, that means :-

• Centroid = (0 , 0)

To find :

Coordinates of the third vertex

Solution :

We know that,

Coordinates of centroid :-

$= ( \dfrac{x1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3} )$

$= > ( \dfrac{x1 + x2 + x3}{3} , \dfrac{y1 + y2 + y3}{3} ) = (0,0)$

Therefore, x3 :-

$= > \dfrac{8 + 9 + x3}{3} = 0$

$= > \dfrac{17 + x3}{3} = 0$

$= > 17 + x3 = 0$

$= > x3 = - 17$

And, y3 :-

$= > \dfrac{7 + 4 + y3}{3} = 0$

$= > \dfrac{11 + y3}{3} = 0$

$= > 11 + y3 = 0$

$= > y3 = - 11$

Hence, The coordinates of the third vertex is (-17 , -11) respectively

Answer 2

Answer:

Step-by-step explanation:

Coordinates of centroid of a triangle are

X= (a1+b1+c1)/3 Y=(a2+b2+c2)/3

0=(8+9+c1)/3. 0 = (7+4+C2)/3

c1= -17 c2=-11

Coordinates of the third vertex of the triangle ==> (-17,-11)