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

Prove that the following points are the vertices of a right-angled isosceles triangle

(0, 0), (5, 5)

and

(- 5, 5)

.

Accepted Answer

Let the given points be $A (0, 0), B (5, 5)$ and $C (- 5, 5)$ .

To show they are vertices of right angled isosceles triangle

We know that, in a right angles triangle one angle should be $90 °$ and isosceles triangle has two equal sides.

Now, using distance formula

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

$A B = \sqrt{(0 - 5)^{2} + (0 - 5)^{2}}$

By squaring on both the side, we get

$A B^{2} = (0 - 5)^{2} + (0 - 5)^{2}$

$= 25 + 25 = 50 - - - - (i)$

$B C = \sqrt{(5 - (- 5))^{2} + (5 - 5)^{2}}$

By squaring on both the side, we get

$B C^{2} = (5 - (- 5))^{2} + (5 - 5)^{2}$

$= 10^{2} + 0 = 100 - - - - (i i)$

$A C = \sqrt{(0 - (- 5))^{2} + (0 - 5)^{2}}$

By squaring on both the side, we get

$A C^{2} = (0 - (- 5))^{2} + (0 - 5)^{2}$

$= 25 + 25 = 50 - - - - (i i i)$

From equation $(i)$ and $(i i i)$

$A B^{2} = A C^{2} = 50 units$

$∴ AB = AC$

From the equation $(i), (i i)$ and $(i i i)$

By using Pythagoras theorem, we get

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

$= 50 + 50 = 100$

Therefore, it is right angle triangle.

Since, $A B = A C$ and $∠ A = 90^{\circ}$ , the $∆ A B C$ is right angled isosceles triangle.

Therefore, $A, B$ and $C$ are the vertices of right angled isosceles triangle.

Hence, proved.

Prove that the following points are the vertices of a right-angled isosceles triangle $(0, 0), (5, 5)$ and $(- 5, 5)$ .

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Prove that the following points are the vertices of a right-angled isosceles triangle (0, 0), (5, 5) and (-5, 5).

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Prove that the following points are the vertices of a right-angled isosceles triangle $(0, 0), (5, 5)$ and $(- 5, 5)$ .