Question

A(,6,y) ,B(-4,4) & C(x,-1) are the vertices of triangle ABC those centroid is the origin. calculate the value of x and y

Answer 1

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Answer 2

The value of x= -2 and y= -3.

Given:

• A triangle ABC.
• A(,6,y) ,B(-4,4) & C(x,-1)
• origin(0,0) is centroid of ∆ABC.

To find:

• Calculate the values of x and y.

Solution:

Formula to be used:

If a triangle ABC have vertices A(x1,y1), B(x2,y2) and C(x3,y3) then coordinates of centroid are

$\bf x = \frac{x_1 + x_2 + x_3}{3}$

and

$\bf y = \frac{y_1 + y_2 + y_3}{3}$

Step 1:

Write the coordinates of vertices.

Let A(6,y) <=> (x1,y1)

B(-4,4) <=> (x2,y2)

C(x,-1)<=> (x3,y3)

Step 2:

Put the values in coordinates of centroid.

$\frac{6 +(- 4) + x}{3} = 0$

or

$\frac{6 - 4+ x}{3} = 0$

or

$2 + x = 0$

or

$\bf x = - 2$

and

$\frac{y + 4 +(- 1)}{3} = 0$

or

$\frac{y + 4 - 1}{3} = 0$

or

$y + 3 = 0$

or

$\bf y = - 3$

Thus,

Value of x=-2 and y=-3.

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