# Coordinate Geometry Class 10 Formulas

Coordinate Geometry Class 10 Formulas are highly important in studying geometry using coordinate systems. Coordinate geometry is the branch of mathematics that establishes the connection between algebra and geometry through lines and curves. It is a vital tool to study geometry using algebra, and understand algebra with the help of geometry. Coordinate geometry formulas are largely applied in different engineering branches and other fields such as navigation, arts and physics.

## List of Coordinate Geometry Class 10 Formulas

The list of the coordinate geometry class 10 formulas is given below:

- 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}]

- Section Formula: ((m
_{1}x_{2}+ m_{2}x_{1})/m_{1}+ m_{2}, (m_{1}y_{2}+ m_{2}y_{1})/m_{1}+ m_{2})

- Area of Triangle = 1/2 * [ x
_{1}(y_{2}- y_{3}) + x_{2}(y_{3}- y_{1}) + x_{3}(y_{1}- y_{2}) ]

## Applications of Coordinate Geometry Class 10 Formulas

- Coordinate Geometry Class 10 Formulas are used in GPS and navigation. The grids of latitudes and longitudes used for GPS are completely based on Coordinate Geometry. Pilots, aircraft controllers, passengers in the flight, persons waiting for the flight will not be able to get the location or position of the aircraft without coordinate geometry.

- Coordinate geometry is used for locating points and finding the distance between two celestial bodies. For example, astrophysicists find the distance between the planets with the help of coordinate geometry.

- The Coordinate Geometry Class 10 Formulas are primarily used to represent the maps on a computer screen. Projected coordinate systems are applied in both two-dimensional (2D) and three-dimensional (3D) cartesian coordinate systems. They are quite useful in defining the shape of features and the geographic location using x- and y-values.

## Tips to Memorize Coordinate Geometry Class 10 Formulas

- The students need to ensure that they understand all important concepts before beginning with memorizing the formulas. They can also seek guidance from their teachers and friends to gain proficiency in learning concepts.

- They can also go through the derivation of these formulas to develop a rock-solid foundation as well as understand the underlying concepts.

- It is important to practice a variety of questions based on median formulas to ensure a thorough conceptual understanding of all important formulas.

## Coordinate Geometry Class 10 Formulas Examples

**Example: **Determine the value of ‘k’, for which the points (7, - 2), (5, 1), (3, k) are collinear.

**Solution: **We know that three points are collinear if they lie on a straight line.

Let P(x₁, y₁) = (7, - 2), Q(x₂, y₂) = (5 , 1) and R(x₃, y₃) = (3, k)

For the above three points to be collinear, we need to prove that the area of the triangle formed by these points is equal to zero.

1/2 [x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)] = 0

By putting the values of vertices, P, Q, and R in the above formula, we get

1/2 [7{1 - k} + 5{k - (- 2)} + 3{(- 2) - 1}] = 0

7 - 7k + 5k + 10 - 9 = 0

- 2k + 8 = 0

k = 4

Hence, the given points are collinear for k = 4

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

## FAQs On Coordinate Geometry Class 10 Formulas

### What are Important Coordinate Geometry Class 10 Formulas?

Some of the most important coordinate geometry class 10 formulas are provided below:

- Distance Formula: D = √[(x
_{2}– x_{1})^{2}+ (y_{2}– y_{1})^{2}] - Section Formula: ((m
_{1}x_{2}+ m_{2}x_{1})/m_{1}+ m_{2}, (m_{1}y_{2}+ m_{2}y_{1})/m_{1}+ m_{2}) - Area of Triangle = 1/2 * [ x
_{1}(y_{2}- y_{3}) + x_{2}(y_{3}- y_{1}) + x_{3}(y_{1}- y_{2}) ]

### How to Find the Distance Between Two Points Using Coordinate Geometry Class 10 Formulas?

We can use the coordinate geometry class 10 formulas to find the distance between points by making a triangle and using the Pythagorean theorem. The distance formula is applied to find the distance between two points in a coordinate plane. The distance formula to calculate the lengths of the sides between points (x1,y1) and (x2,y2), is D = √[(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2} ].

### Why is it Important to Solve Various Problems Based on the Coordinate Geometry Class 10 Formulas?

Students should solve maximum questions based on Coordinate Geometry Class 10 Formulas as it will help them in understanding all core concepts and their applications. Getting well versed with these concepts will enable students to identify and derive different formulas which are to be applied in the questions.

### How to Memorize the Coordinate Geometry Class 10 Formulas?

One of the most effective ways to learn and memorize Coordinate Geometry Class 10 Formulas is to apply them in solving various types of problems. While applying these formulas students will form a clear base to understand and derive formulas. It will be helpful for them in quickly revising them during exams.

### How to Download Coordinate Geometry Class 10 Formulas pdf?

Students can easily download the Coordinate Geometry Class 10 Formulas by clicking on the download option provided on the page. On clicking the option, a popup will appear. Students need to provide a valid phone number to receive OTP. Once the OTP is entered the pdf file will automatically download on the device.

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