Two vertices of a triangle are $(1, 2), (3, 5)$ and its centroid is at the origin. Find the coordinates of the third vertex.

Given:

Two vertices of a triangle are $(1, 2), (3, 5)$ and its centroid is at the origin.

To do:

We have to find the coordinates of the third vertex.

Solution:

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

We know that,

Coordinates of the centroid of a triangle are $(\frac{Sum\ of\ abscissa}{3}, \frac{Sum\ of\ ordinates}{3})$

Therefore,

The coordinates of the centroid of the given triangle are,

$(0,0)=(\frac{1+3+x}{3}, \frac{2+5+y}{3})$

$(0,0)=(\frac{4+x}{3}, \frac{7+y}{3})$

On comparing, we get,

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

$0(3)=4+x$

$x=0-4$

$x=-4$

$0=\frac{7+y}{3}$

$0(3)=7+y$

$y=0-7$

$y=-7$

The coordinates of the third vertex are $(-4, -7)$.

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Updated on: 10-Oct-2022

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