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# Distance Formula Class 10

Distance formula class 10 is applied to calculate the distance between two points. Students must understand the core concept of the distance formula in coordinate geometry as it is one of the most important formulas of class 10 math. The applications of the distance formula can be seen in various spheres to estimate the distance of moving objects or things from one point to another.

## List of Distance Formula Class 10

Here is a list of the Distance formulas for class 10.

- Distance Formula to find distance between two points (x
_{1},y_{1}) and (x_{2},y_{2}) is D = √[(x_{2}– x_{1})^{2}+ (y_{2}– y_{1})^{2}]. - The distance formula to find the distance of a point P(x, y) from the origin O(0,0) is D = √((x
_{2}+ y_{2}). - Coordinates of point P(x, y) that divides the line segment joining the points A(x
_{1}, y_{1}) and B(x_{2}, y_{2}) internally in the ratio m1: m2 are m_{1}x_{2}+ m_{2}x_{1}/m_{1}+ m_{2}and m_{1}x_{2}+ m_{2}x_{1}/m_{1}+ m_{2} - The mid-point of the line segment joining the points A(x
_{1}, y_{1}) and B(x_{2}, y_{2}) can be found by [(x_{1}+ x_{2}/2) , (y_{1}+ y_{2})/2].

## Applications of Distance Formula Class 10

Distance formula class 10 has its applications in algebra as well as geometry. Some more applications of distance formula class 10 as can be seen below:

- The distance formula is applied to find the coordinates of two points in the sea and on land. The derivation of the distance formula is based on the Pythagoras theorem and thus serves as an integral part of the navigation system.
- The distance formula is very useful in coordinate geometry itself. If the coordinates of a quadrilateral are given, we can use the distance formula to ascertain whether the quadrilateral is a square or not. If the sides of the quadrilateral are equal, it would be a square. In coordinate geometry wherever the shortest path between two points is required, the distance formula comes in handy.

## Distance Formula class 10 Examples

**Example 1:** Use the distance formula to find the distance between the point P(-5,7) and Q(-1,3).

**Solution:** Distance between two points is given by formula = √[(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2} ]

Therefore, the distance between P(- 5, 7) and Q(- 1, 3) is given by

d = √[( -1 + 5 )^{2} + (3 - 7)^{2}]

= √(4)^{2} + (- 4)^{2}

= √16 + 16

= √32

= 4√2

**Example 2:** Determine the coordinates of the point that divides the line segment joining the points (4, – 2) and (7, 4) in the ratio 2 : 1 internally.

**Solution:** Let us consider that the coordinates of the point are (x,y)

By using the section formula, we get

(x ) = ( m_{1}*x_{2}+m_{2}*x_{1}/m_{1}+m_{2}) = (4*2 + 7*1)/3 = 5

(y) = (m_{1}*y_{2} +m_{2}*y_{1})/m_{1} + m_{2} = (-2 * 2 + 4 * 1)/3 = 0

Hence, the coordinates are (5,0).

## Tips to Memorize Distance Formula Class 10

Memorizing the distance formula class 10 is important for students to solve various types of questions based on them. Here are a few simple tips for students to remember formula easily:

- Students should have a sound knowledge of all concepts related to distance formulas class 10. It will benefit them in applying the formula logically to solve various problems.
- Students should aim to solve plenty of problems based on the distance formula. This will help them to enhance their understanding of the distance formula to apply it in the various scenarios.
- Students can various resources available on the internet like formula sheets to learn and revise these formulas. They can download these formula sheets on their mobiles, tablets and laptops to revise them anytime.

Students can download the printable **Maths Formulas Class 10** sheet from below.

## FAQs on Distance Formulas for Class 10

### What are the Important Formulas Covered Under Distance Formula Class 10?

The important distance formulas for class 10 are listed as follows:

- The distance between P(x1 , y1 ) and Q(x
_{2}, y_{2}) is √[(x_{2}– x_{1})^{2}+ (y_{2}– y_{1})^{2}] - The distance of a point P(x, y) from the origin is given by √(x2 + y2)
- The coordinates of the point P(x, y) which divides the line segment joining the points P(x
_{1}, y_{1})and Q(x_{2 }, y_{2}) internally in the ratio m1 : m2 are (m_{1}x_{2}+ m_{2}x_{1})/(m_{1}+m_{2}) , (m_{1}y_{2}+ m_{2}y_{1})/(m_{1}+m_{2}) - The mid-point of the line segment joining the points P(x1 , y1 ) and Q(x
_{2}, y_{2}) can be found by [( x_{1}+ x_{2}) /2 (y_{1}+ y_{2})/2]

### What are the Basic Formulas in Distance Formula Class 10?

The basic formulas in distance formula class 10 are listed in this article. Students must focus on understanding each and every term used in these formulas. The examples and practical tips summarized in this article will help the students to remember these formulas easily.

### What are the Important Formulas Covering Distance Formula Class 10?

The important formulas covering distance formula class 10 listed in this article will help students to learn how to find the distance between two points, and distance of a point from a line, as well as midpoints and section division ratio of lines.

### How Many Formulas are There in Distance Formula Class 10?

There are around three to four main formulas covered under distance formula class 10. Solving and practicing problems based on these formulas, will simplify the concept of coordinate geometry for the students. These formulas give a detailed insight into how two-dimensional coordinate geometry is a mix of algebra and geometry. The emphasis is on representing a line algebraically, with the slope being the most significant factor.

### How can I Memorize distance Formula class 10?

To memorize distance formula class 10 the students must thoroughly understand the theory part present in the chapter. Reading notes and clearing all the doubts will help you to practice better. Once you gain an understanding of the theory part try to apply them in solving all the examples and problems.

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