Question

5. If (-3,0,3) is a centroid of a triangle for
which (3,-9,11) ,(-2,5,7) are two
vertices , then third vertex is​

Answer 1

Answer:

$\large\bold\red{(-10,4,-9)}$

Step-by-step explanation:

Let's assume a triangle ∆ABChaving centroid G.

Now,

According to question,

Coordinates of,

• A = (3,-9,11)
• B = (-2,5,7)
• G= (-3,0,3)

Let,

The coordinate of C is (x,y,z)

Now,

We know that,

• Sum of all x, y, and z coordinates of vertices, each divided by 3 equals to x, y and z Coordinate of the centroid respectively.

Therefore,

We get,

$= > \frac{3 + ( - 2) + x}{3} = - 3 \\ \\ = > 3 - 2 + x = - 9 \\ \\ = > x + 1 = - 9 \\ \\ = > x = - 9 - 1 \\ \\ = > \large \boxed{ x = - 10}$

Similarly,

We get,

$= > \frac{ - 9 + 5 + y}{3} = 0 \\ \\ = > - 9 + 5 + y = 0 \\ \\ = > y = 9 - 5 \\ \\ = > \large \boxed{ y = 4}$

And,

Also,

We get,

$= > \frac{11 + 7 + z}{3} = 3 \\ \\ = > 18 + z = 9 \\ \\ = > z = 9 - 18 \\ \\ = > \large \boxed{ z = - 9}$

Hence,

The thirs vertex is (-10,4,-9)