Question

In ΔABC, G (-4,-7) is the centroid. If A (-14,-19) and B(3,5) then find the co-ordinates of C.

Answer 1

We know, if vertices of triangle are (x₁ , y₁) , (x₂, y₂) and (x₃, y₃)
Then, centroid of triangle is given by {(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 }

Here, centroid of triangle ABC is G ≡ (-4, -7)
A ≡ (-14, - 19) , B ≡ ( 3, 5)
Let C ≡ (x , y)

so, G ≡ (-4, -7) ≡ {(-14 + 3 + x)/3 , (-19 + 5 + y)/3 }
-4 = (-14 + 3 + x)/3
⇒-4 × 3 = -11 + x
⇒-12 + 11 = x
⇒x = -1

-7 = (-19 + 5 + y)/3
⇒-7 × 3 = (-19 + 5 + y)
⇒ -21 = -14 + y
⇒-21 + 14 = y
⇒y = -7

$\bf{point C = (-1,-7)}$

Answer 2

REFER THE ATTACHMENT

HOPE IT HELPS U !!!!