Name: Coordinates of Centroid
Uploaded: 2019-07-19
Duration: 3 min 16 s
Description: This video discusses how we can find the coordinates of the centroid using the coordinates of the three vertices given. Watch and learn the concept.

Question

Find the circumcentre of the triangle whose vertices are

(- 2, - 3), (- 1, 0)

and

(7, - 6)

Accepted Answer

Let the given vertices of triangle be $A (- 2, - 3), B (- 1, 0) and C (7, - 6)$

To find the circumcenter of the triangle.

Circumcircle is a circle passes through all the three vertices of triangle.

Using distance formula

Distance $= \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

$A B = \sqrt{(- 2 - (- 1))^{2} + (- 3 - 0)^{2}} = \sqrt{1 + 9} = \sqrt{10}$

$B C = \sqrt{(- 1 - 7)^{2} + (0 - (- 6))^{2}} = \sqrt{64 + 36} = \sqrt{100}$

$A C = \sqrt{(- 2 - 7)^{2} + (- 3 - (- 6))^{2}} = \sqrt{81 + 9} = \sqrt{90}$

By pythagoras theorem,

$A B^{2} + A C^{2} = B C^{2}$

That is, ${(\sqrt{100})}^{2} = {(\sqrt{10})}^{2} + {(\sqrt{90})}^{2}$

$\Rightarrow 100 = 10 + 90$

$\Rightarrow 100 = 100$

Therefore, the $∆ ABC$ is a right angled triangle, right angled at $A$ .

In the above figure, the side $B C$ of $∆ A B C$ is the diameter of circle.

Since, $B C = 10$ units

The radius of the circle $= \frac{B C}{2} = \frac{10}{2} = 5$ units.

Now, let $O (x, y)$ be the circumcenter of the circle

Using midpoint formula,

$(x, y) = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Circumcenter is the midpoint of the vertices $B$ and $C$ , that is

$x = \frac{- 1 + 7}{2} = 3, y = \frac{0 - 6}{2} = - 3$

Therefore, $O (3, - 3)$ is the circumcenter of the circle.

Find the circumcentre of the triangle whose vertices are $(- 2, - 3), (- 1, 0)$ and $(7, - 6)$

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Find the circumcentre of the triangle whose vertices are (-2,-3), (-1, 0) and (7,-6)

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Find the circumcentre of the triangle whose vertices are $(- 2, - 3), (- 1, 0)$ and $(7, - 6)$