Question

Find out the third vertex of the triangle if Vertex - 1 (8,6) Vertex - 2 = (-2, 6) Centroid = (8,4) A. О (10,-2) B.O (20,-2) C. O (10,2) D. O (180)​

Answer 1

Step-by-step explanation:

Let the third vertex of the triangle be C(x,y) and the other vertices A(-3,1) and B(0,-2).

Coordinates of the centroid of the triangle = (0,0)

∴ (-3+0+x / 3, 1-2+y / 3) = (0,0)

-3+x = 0

x = 3

And - 1 + y = 0

y = 1

∴ The third vertex of the triangle is (3,1)

Answer 2

Answer:

The third vertex is (18,0)

Step-by-step explanation:

Given:

Vertex 1 = (8, 6)

Vertex 2 = (-2, 6)

Centroid = (8, 4)

To find:

Vertex 3

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

We know:

Centroid of a triangle = $(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})$

where (x₁, y₁) = coordinates of first vertex

          (x₂, y₂) = coordinates of second vertex

          (x₃, y₃) = coordinates of third vertex

Method:

Using the formula of centroid of triangle, we get,

(8, 4) =  $(\frac{8+(-2)+x}{3}, \frac{6+6+y}{3})$

=> (8, 4) =  $(\frac{6+x}{3}, \frac{12+y}{3})$

On equating, we get,

8 = $\frac{6+x}{3}$  and 4 = $\frac{12+y}{3}$

=> 6 + x = 24   and  12 + y = 12

=> x = 24 - 6    and  y = 12 - 12

=> x = 18           and y = 0

Therefore, the third vertex is (18,0)