Question

A (-4,4), B (x, -1) and C (6,y) are the vertices of ∆ABC. If the centroid of this triangle ABC is at the origin, find the values of x and y

Answer 1

Answer:

answer for the given problem is given

Answer 2

Concept

The centroid of this triangle is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3} )$.

Where$(x_1,y_1), (x_2,y_2) \text{ and } (x_3,y_3)$ are the vertices of triangle.

Given

The points A (-4,4), B (x, -1) and C (6,y)  are the vertices of ∆ABC

To find

We have to find the values of x and y if the centroid of this triangle ABC is at the origin.

Solution

Apply the centroid formula

Centroid $=(\frac{-4+x+6}{3},\frac{4-1+y}{3} )$

The centroid of this triangle ABC is at the origin.

$(0,0)=(\frac{x+2}{3},\frac{3+y}{3} )$

So,

$\frac{x+2}{3}=0\\ x+2=0\\x=-2$

and

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

Hence the value of $x=-2\text{ and } y=-3$.