# Xam Idea Class 10 Maths Chapter 6 Solutions: Coordinate Geometry

Xam Idea Class 10 Maths Solutions for Chapter 6 ‘Coordinate Geometry’ help you understand the various concepts of the chapter. In this chapter of Xam Idea solutions, you will study many important concepts like distance formula, section formula, methods to find the area of a triangle including discussion about collinearity of 3 points. These concepts are deeply discussed in the chapter so that you are able to study thoroughly each concept for your Class 10 board exams.

After studying from the Xam Idea Class 10 Maths Solutions for Coordinate Geometry, you will be able to answer questions related to finding whether a point lies on a line or not or how the diagonals of a rectangle intersect each other. The exercise of the chapter consists of a total number of 56 questions. The exercise is divided into 6 sections and the questions in each section are framed accordingly based on the CBSE exam pattern. This includes short answer questions, long answer questions, higher-order thinking skills, and value-based questions.

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## Important Topics For Xam Idea Class 10 Maths Solutions Chapter 6: Coordinate Geometry

**The Cartesian System of Coordinates**

As per the figure given above, there are two perpendicular lines meeting at a point O. This is known as the Cartesian System of Coordinates where the horizontal line represents the x-axis and the vertical line represents the y-axis. These axes are also known as coordinates.

The points of the y-axis or the y-coordinate are known as **ordinates**. So, the ordinate is the distance of a given point from the x-axis. The points of the x-axis are known as the **abscissa**. So, the abscissa is the distance of a given point from the y-axis.

The Cartesian coordinate system is divided into 4 different quadrants where the values of x and y-axis very positively and negatively. The four quadrants are clearly depicted in the image given below.

**The Distance Formula**

If the coordinates of two points arethen we use the distance formula to calculate their distance such asThe value of the distance is always positive.

**The Section Formula**

If a given line segment with endpoints A(x1, y1)and B(x_{2}, y_{2}) is divided by a point P internally into a ratio m_{1}:m_{2}, then point p coordinates are given byHowever, if a line segment with endpointsandand we are required to find its midpoint the given coordinates will be

**Area of a Triangle**

If the coordinates of the three vertices of a triangle are A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}), then the area of a triangle ABC will be given by:

### Exercise Discussion of Xam Idea Class 10 Maths Solutions Chapter 6: Coordinate Geometry

**Very short answer type questions**

In this section, there are a total number of 10 questions in this section. These questions are to be answered in one word, or one sentence, as per the questions demand. The questions cover the very basic concept of the chapter and are not that complex. While solving this section you will face questions like what is the area of a triangle formed by the given points or if the centroid of the triangle formed by the given points is at the origin then what is the value of a+b+c.

**Short answer type questions- I**

There are overall 14 questions in this section. In the first part of short questions, you will find the coordinates, ratios, distance between points and value of variables. You will have to answer questions like finding the values of x for which the distance between the given points is 10.

**Short answer type questions-II**

There are a total number of 24 questions in this part of short questions. The questions in this are based on finding the distance between points, determining if the points are collinear, and finding relations between points. You will have to answer questions in this section such as- find the point on the x-axis which is equidistant from the given points and so on.

**Long answer type questions**

In this section, there are overall 11 questions which need a proper explanation of how you solved the question. In this part you will answer questions like- find the area of a triangle formed by joining the midpoints of the triangle whose vertices are given. Also, find the vertices of this area to the area of a given triangle.

**Higher-order thinking skills**

In this section, there are a total of 5 questions. To find solutions to these questions you are required to study the chapter to its core. These contain questions to challenge your brain up to a level. The questions in this section are such as- if the coordinates of a midpoint of the sides triangle are given, find its centroid or find the centre of a circle passing through the points x, y and z.

**Value-based questions**

There are just 2 questions in this section in which you also have to answer the general value that the question depicts. These types of questions help to learn values that you learn while solving the questions. For instance, in one question, you have to find the area of a region covered by a group of students for their campaign about ‘say no to plastic’. You also have to state the harmful effects of using plastic and how can you spread awareness of such a campaign.

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