Coordinate Geometry
All
Guides
Practice
Learn

# NCERT Solutions for Class 10 Maths Chapter 7 : Coordinate Geometry

Coordinate Geometry Class 10 Maths NCERT Solutions Chapter 7  is concerned with the understanding of various aspects of coordinate geometry. Students preparing for chapter 7 maths class 10 will be able to clear all their concepts on coordinate geometry at the root level. It allows us to learn geometry with algebra and understand algebra with geometry. Expert faculty of Toppr produced these solutions to assist students with their first term exam preparations. It covers all major concepts in detail, allowing students to understand the ideas better.

Class 10 Maths chapter 7 NCERT Solutions Coordinate Geometry of the section, concentrates on the essential concepts such as the distance computation between two locations in the cartesian plane, internal and external division of a line segment in a specific ratio, area calculation of a triangle, and real-world applications of these formulas. All of these solutions are designed with the new CBSE pattern in mind so that students have a complete understanding of their tests.

Class 10 Coordinate Geometry Questions and Answers are very useful for getting good grades in tests and properly preparing you with all of the important concepts. These NCERT Solutions are valuable tools that can assist you not only in covering the full syllabus but also in providing an in-depth analysis of the subjects. The NCERT Solutions for Class 10 Maths Chapter 7 are available in pdf format below, and some of them are also included in the exercises.

Table of Content
Learn with Videos
>

## Access NCERT Solutions for Class 10 Maths Chapter 7 : Coordinate Geometry

Exercise 7.1
Question 1
Find the distance between the following pairs of points :
i)
ii)
iii)
Medium
Solution
Verified by Toppr
D units
D units
D units
Question 3
Determine if the points and are collinear , by distance formula.
Medium
Solution
Verified by Toppr
Now,
As,
If points are collinear then
But
So they are not collinear.
Question 4
Check whether , and are the vertices of an isosceles triangles.
Easy
Solution
Verified by Toppr
Let ABC be the triangle
By distance formula
Since
Hence & are vertices of isosceles triangle.
Question 5
In a classroom, friends are seated at the points , and as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, "Don't you think is a square " ? Chameli disagrees. Using distance formula, find which of them is correct.
Medium
Solution
Verified by Toppr
From the figure co-ordinates of points can be expressed as shown below,

Four sides of the quadrilateral are equal

Therefore is a square

Therefore, Champa is correct between two
Question 6
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i)
(ii)
(iii)
Medium
Solution
Verified by Toppr
(i) Let the given points are , , and Then,

Since the four sides and are equal  and the diagonals and are equal .

(ii)Let the given points are ,, and Then
Here

(iii)Let the given points are ,, and Then

Here . But
Hence the pairs of opposite sides are equal but diagonal are not equal so it is a parallelogram.

Question 7
Point on the -axis which is equidistant from and is:
A
B
C
D
Medium
Solution
Verified by Toppr
Since point on axis, then coordinate of the point is
According to the question this point  is equidistant from the points and .
That is, distance from   and  distance from  and .

So, point is .
Question 8
Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.
A
8, 2
B
-9, 3
C
-9, 5
D
-8 , 2
Medium
Solution
Verified by Toppr

Squaring both sides,

Question 9
If is equidistant from and , find the values of . Also find the distances and .
Medium
Solution
Verified by Toppr
As given   is equidistant from and

[ By using disatnce formula ]

Distance between and

Distance between and

Question 10
Find a relation between and such that the point is equidistant from the point and .
Medium
Solution
Verified by Toppr
Let the point is equidistant from the points and

By using the distance formula

we have

Hence this is a relation between and .
View more
Practice more questions

### NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry – Brief Overview

#### 1. Coordinates

The x-coordinate, or abscissa, of a point, is its distance from the y-axis. The y-coordinate, or ordinate, of a point, is its distance from the x-axis. A point on the x-axis has coordinates of the form (x, 0), while a point on the y-axis has coordinates of the form (0, y).

#### 2. Coordinate Geometry

Coordinate geometry is the branch of mathematics that uses algebraic methods to solve geometrical issues. It is the study of cartesian coordinates. This system is typically used to alter the equations of two-dimensional shapes such as triangles, squares, circles, and so on.

Coordinate geometry is significant in mathematics because it allows us to identify points on any given plane. Coordinate geometry is also known as the study of graphs. It also has numerous applications in trigonometry, dimensional geometry, calculus, and other sciences.

#### 3. Distance Formula

The distance between any two points, P(x1, y1) and Q(x2, y2) in the plane are given by:

Also, the distance between P(x1, y1) and the origin is:

#### 4. Section Formula

The section formula assists us in determining the coordinates of the point that divides the line in the ratio m:n. If P is the point splitting the line AB internally in the ratio m:n where A(x1, y1) and B(x2, y2).

P's coordinates will be:

If P is the point splitting the line AB externally in the ratio m:n where A(x1, y1) and B(x2, y2).

P's coordinates will be:

#### 5. Area of Triangle

The area of ∆ABC formed by the vertices A(x1, y1), B(x2, y2), C(x3, y3) is given by:

Area of Triangle = ½ x [x1(y2 - y3) + x2(y3 - y1) + x3(y1 – y2)]

Related Chapters

### Frequently Asked Questions on NCERT Class 10 Maths Chapter 7 : Coordinate Geometry

Q1. What are the most important topics in NCERT Class 10 Chapter 7 Coordinate Geometry?

Answer: The distance formula, the section formula, and the area of the triangle are all important concepts in class 10 chapter 7 Coordinate Geometry. Questions on all three topics carry a considerable weightage in tests, therefore students should practice them thoroughly.

Q2. How many exercises are there in Chapter 7 of Class 10 Maths?

Answer: There are four exercises in total. Class 10 Maths Chapter 7 Coordinate Geometry has 33 problems, 20 of which are pretty easy, 7 of which are moderately tough, and 6 of which are long answer intricate sums. These questions are spread among four exercises in this chapter. They are both theoretical and practical in character, based on the cartesian plane and the associated formulas.

Q3. What is the purpose of Coordinate Geometry?

Answer: Coordinate geometry has many uses in everyday life. It is an important part of mathematics that helps us locate points on a plane. Furthermore, it has several applications in trigonometry, calculus, dimensional geometry, and other sciences. A few examples of coordinate geometry applications are: GPS positions in digital maps to pinpoint exact locations, Coordinate geometry is also employed in the construction of highways, buildings, and other structures, and Coordinate geometry is also employed in the cartographic representation of 2D and 3D objects.

Related Chapters