The distance between two points is calculated using the formula

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

**Example1:** Find the distance between the points (*1, -3*) and the point (*5, -8*)

**Solution:**
The distance between the points A and B is given by the formula

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

Here A= (1, -3) = (x1, y1) and B= (5, -8) = (x2, y2). Now apply this formula

$$\sqrt{{(5- 1)^{2}} +(-8 + 3)^{2}}$$

$$\sqrt{{(4)^{2}} +(-5)^{2}}$$

$$\sqrt{16 + 25}$$

$$\sqrt{41}$$

**Example 2:** Find the distance between the points (*2, -7*) and (*3, 2*)

**Solution:**
The distance between the points A and B is given by the formula

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

Here A= (1, -3) = (x1, y1) and B= (5, -8) = (x2, y2). Now apply this formula

$$\sqrt{{(3- 2)^{2}} +(2 + 7)^{2}}$$

$$\sqrt{{(1)^{2}} +(9)^{2}}$$

$$\sqrt{1+ 81}$$

$$\sqrt{82}$$

**Example3:** Find the distance between the points (*a, b*) and (*-a, -b*).

**Solution:**
The distance between the points A and B is given by the formula

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

Here A= (*1, -3*) = (*x1, y1*) and B= (*5, -8*) = (*x2, y2*). Now apply this formula

$$\sqrt{{(-a- a)^{2}} +(-b -b)^{2}}$$

$$\sqrt{{(-2a)^{2}} +(-2b)^{2}}$$

$$\sqrt{4a^2 +4b^2}$$

$$2 \sqrt{a^2+b^2}$$

** Median**
: A median is a line segment joining a vertex to a midpoint to the opposite side of the triangle.

** Centroid**
: The intersection of 3 medians of the triangle is called the centroid of the triangle

The formula for centroid is given by

$$[ \frac{(x_{1}+x_{2}+x_{3})}{3}, \frac{(y_{1}+y_{2}+y_{3})}{3} ]$$

**Examples:**

**Find the centroid of the triangle with the points ( 1, 2), (3, 5), (7, 8)**

We have the formula

$$[ \frac{(1+3+7)}{3}, \frac{(2+5+8)}{3} ]$$

$$(\frac{11}{3}, \frac{15}{3}) = ((\frac{11}{3}, 5)$$

**Find the centroid of the triangle with the points ( 5, 2), (6, 5), (-7, 8)**

We have the formula

$$[ \frac{(5+6-7)}{3}, \frac{(2+5+8)}{3} ]$$

$$(\frac{4}{3}, \frac{15}{3}) = ((\frac{4}{3}, 5)$$

**Find the centroid of the triangle with the points ( 0, 2), (6, 1), (-7, 3)**

We have the formula

$$[ \frac{(0+6-7)}{3}, \frac{(2+1+3)}{3} ]$$

$$(\frac{-1}{3}, \frac{7}{3})$$

The above three examples show us how to calculate the centroid.

**Ortho Centre:**
The position where the 3 altitudes of a triangle meet is called the Ortho Centre of the triangle.

The below diagram shows all the above points:

**Average Acceleration Calculator**

Average acceleration is the object's change in speed for a specific given time period. ...

When an object falls into the ground due to planet's own gravitational force is known a...

In Mathematics, the permutation can be explained as the arrangement of objects in a particular order. It is an ordered...

A rectangle can be explained as a 4-sided quadrilateral which contains equal opposite sides. In a rectangle

A three sided polygon which has three vertices and three angles is called a triangle. Equilateral triangle...