# Distance Formula Class 9

Students often get confused with the distance formula and with the formula of distance and speed. It is important to understand that in co-ordinate geometry, the ‘distance formula’ is used to calculate the distance between any two points, while distance and speed comes under another topic of speed, distance and time. This article contains a list of distance formulas for class 9 along with some easy tips to remember them.

## List of Distance Formula Class 9

Here is a brief list of the formulas related to the distance formula.

- The distance between coordinate P(x
_{1}, y_{1}) and coordinate Q(x_{2}, y_{2}) is calculated using the distance formula: d = √[(x_{2}- x_{1})^{2}+ (y_{2 }- y_{1})^{2}] - The distance of a point P(x, y) from the origin is given by √(x
_{2}+ y_{2}) - The midpoint of the line segment joining the points P(x
_{1}, y_{1}) and Q(x_{2}, y_{2}) can be found using the formula, [(x_{1 }+ x_{2}) / 2 , (y_{1 }+ y_{2}) / 2]

## Applications of Distance Formula Class 9

The distance formula class 9 has its applications in algebra and geometry as shown below:

- Distance formula is derived from the Pythagoras theorem and is very useful in estimating distances and thus serves as an integral part of the navigation strategy. For example, we can use the distance formula to know the distance between the source and the destination and can even find the shortest possible route.

- Distance formula proves very useful in co-ordinate geometry itself. For example, 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 all the sides are of equal length it would be a square.

## Distance Formula Class 9 Examples

**Example 1 : **Find the distance between the following points, A(2,4) and B(-4,4)

**Solution : **Distance between the given points (d) = √[(x_{2} - x_{1})^{2} + (y_{2 }- y_{1})^{2}]. Here, x_{1} = 2, x_{2} = -4; y_{1} = 4, and y_{2 }= 4. Substituting the values in the formula,

= √[( -4 - 2)^{2} + (4 - 4)^{2}]

= √[( -6)^{2} + (0)^{2}] = √[(36)]

= 6 units

**Example 2 : **Find the midpoint of the line segment joining the points P(4 , 4) and Q(6 , 8).

**Solution: **The midpoint of the line segment can be calculated using the formula, Midpoint = [(x_{1 }+ x_{2}) / 2 , (y_{1}+ y_{2}) / 2]. Here, x_{1}= 4, x_{2} = 6, y_{1} = 4, and y_{2}= 8. Substituting the values in the formula, Midpoint = [(x_{1 }+ x_{2})/2 , (y_{1}+ y_{2})/2]

Midpoint = [(4 + 6)/2, (4 + 8)/2] = [10/2; 12/2] = (5,6)

Therefore, the coordinates of the midpoint are (5,6).

## Tips to Memorize Distance Formula Class 9

The following tips can be helpful for the students to remember the distance formula:

- Students must seek clarification from their teachers or friends for even the tiniest of doubts. They must not be afraid to express their doubts, since this will only lead to additional confusion in the future when it comes to grasping complex topics. Clearing up any uncertainties at this step would help in understanding the underlying logic of the formula, making it easier to recall.
- Students should strive to practice as many formula-based problems as possible. This allows students to become familiar with the various scenarios in which a single formula can be applied in several ways, allowing them to recall them quickly when needed.

- In the current technological age, students use gadgets such as mobile phones and laptops, so they can save these formulas as wallpapers. This will result in looking at the formula wallpaper whenever they use their device giving a quick revision.

Students can download the printable **Maths Formulas Class 9** sheet from below.

## FAQs on Distance Formulas for Class 9

### What are the Important Distance Formulas for Class 9?

The important distance formulas for class 9 are listed below:

- The distance between coordinate P(x
_{1}, y_{1}) and coordinate Q(x_{2}, y_{2}) is calculated using the distance formula: d = √[(x_{2}- x_{1})^{2}+ (y_{2 }- y_{1})^{2}] - The distance of a point P(x, y) from the origin is given by √(x
^{2}+ y^{2}) - The midpoint of the line segment joining the points P(x
_{1}, y_{1}) and Q(x_{2}, y_{2}) can be found using the formula, [(x_{1 }+ x_{2}) / 2 , (y_{1 }+ y_{2}) / 2]

### What are the Basic Formulas in Distance Formula Class 9?

The basic formulas covered in the distance formula class 9 as listed in this article form the basis for many concepts of algebra and trigonometry. Hence, it is essential for the students to focus on understanding these well. The examples and practical tips summarized in this article will help the students to revise their formulas thoroughly without any stress.

### What are the Important Formulas Covering Distance Formula Class 9?

The important formulas covering distance formula class 9 that are also listed in this article are as follows.

- The distance between coordinate P(x
_{1}, y_{1}) and coordinate Q(x_{2}, y_{2}) is calculated using the distance formula: d = √[(x_{2}- x_{1})^{2}+ (y_{2 }- y_{1})^{2}] - The distance of a point P(x, y) from the origin is given by √(x
_{2}+ y_{2}) - The midpoint of the line segment joining the points P(x
_{1 }, y_{1}) and Q(x_{2}, y_{2}) can be found using the formula, [(x_{1 }+ x_{2}) / 2 , (y_{1}+ y_{2}) / 2]

These formulas will help students learn how to find the distance between two points, and distance of a point from a line, as well as midpoints.

### How Many Formulas are there in Distance Formula Class 9?

There are three basic distance formulas, which, if learned well, will simplify the concept of coordinate geometry for the students. These formulas give a detailed insight into how the two-dimensional co-ordinate 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 9?

To memorize distance formula class 9 the students can use the following tips:

- Go through the theory presented in the chapter thoroughly and note down all the doubts so as to get them cleared with the help of teachers or friends. If the basics will be clear there will be no difficulty in understanding the formulas.

- Once the theoretical part is clear, the students must try to do all the solved examples and then move to the exercise questions. This will help in giving a good practice of the usage of the formulas in different contexts.

- Students can also take help of their mobiles and laptops in the learning process. The images of formulas can be set as wallpaper on these devices to ensure having a glance at them throughout the day.

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