Question

two vertics of a triangle are (1,4) and (3,1) if the centroid of the triangle is origin find the third vertex​

Answer 1

Answer:

(-4, -5)

Step-by-step explanation:

Given, centroid of the triangle is origin i.e G(0,0).

Let the coordinates of third vertex be (x,y)

(x₁,y₁) = (1,4), (x₂,y₂) = (3,1), (x₃,y₃) = (x,y)

The Coordinates of centroid of triangle are,

∴ (x₁ + x₂ + x₃/3, y₁ + y₂ + y₃/3)

x = (1 + 3 + x)/3

=> 0 = (1 + 3 + x)/3

=> x + 4 = 0

=> x = -4

and,

y = (4 + 1 + y)/3

=> 0 = (5 + y)/3

=> 5 + y = 0

=> y = -5

Thus, the third vertex is (-4,-5)

Hope it helps

Answer 2

$\boxed{\boxed{\mathtt{Answer = -4, -5}}}$

Solution : Let the coordinate of third vertex are (h, k)

Therefore the coordinates of centroid of the triangle is $(\frac{1+3+h}{3},\frac{4+1+k}{3})$

Now, According to the question we know that the centroid of the given triangle is form origin is (0, 0)

Therefore, $\frac{1+3+h}{3}=0\:and \: \frac{4+1+k}{3}=0$

$\implies$ 1+3+h = 0

$\implies$ 4+h =0 = h= ―4 and

$\implies$ 4+1+k = 0

$\implies$ 5+k = 0 = k = ―5

Therefore the third vertex of given triangle are (―4, ―5).