Get Free **NCERT Solutions for Class 10 Maths Chapter 7** Ex 7.1 Coordinate Geometry Class 10 Maths NCERT Solutions are extremely helpful while doing homework. Exercise 7.1 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in **Chapter 7 Maths Class 10 Coordinate Geometry** Exercise 7.1 Provided in NCERT Textbook

**Topics and Sub Topics in Class 10 Maths Chapter 7 Coordinate Geometry:**

Section Name | Topic Name |

7 | Coordinate Geometry |

7.1 | Introduction |

7.2 | Distance Formula |

7.3 | Section Formula |

7.4 | Area of a Triangle |

7.5 | Summary |

- Coordinate Geometry Class 10 Ex 7.1
- Coordinate Geometry Class 10 Ex 7.2
- Coordinate Geometry Class 10 Ex 7.3
- Coordinate Geometry Class 10 Ex 7.4
- Extra Questions for Class 10 Maths Coordinate Geometry

## NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1.

Board | CBSE |

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 7 |

Chapter Name | Coordinate Geometry |

Exercise | Ex 7.1 |

Number of Questions Solved | 10 |

Category | NCERT Solutions |

Question 1.

Find the distance between the following pairs of points:

(i) (2, 3), (4, 1)

(ii) (-5, 7), (-1, 3)

(iii) (a, b), (-a, -b)

Solution:

Question 2.

Find the distance between the points (0, 0) and (36, 15).

Solution:

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Question 3.

Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Solution:

Question 4.

Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

Solution:

Question 5.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the given figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

Solution:

Question 6.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.

(i) (-1, -2), (1, 0), (-1, 2), (-3, 0)

(ii) (-3, 5), (3, 1), (0, 3), (-1, -4)

(iii) (4, 5), (7, 6), (4, 3), (1, 2)

Solution:

Question 7.

Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).

Solution:

Question 8.

Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.

Solution:

Question 9.

If Q (0, 1) is equidistant from P (5, -3), and R (x, 6), find the values of x. Also, find the distances QR and PR.

Solution:

Question 10.

Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4).

Solution:

### Class 10 Maths Coordinate Geometry Mind Maths

#### Coordinate of a Point in XY – Plane

The Perpendicular distance of x a point from the y-axis is called its x-coordinate or abscissa. The perpendicular distance y of a point from the x-axis is called its y-coordinate or ordinate. The x and y taken together in order is called coordinte of point denoted by (x, y).

The coordinate of the points on x-axis are of the form (x, 0) and the points on the y-axis are of the form(0, y). Coordinate of origin is (0, 0).

#### Sign-conventions in the XY-Plane

The x and y-axis divide the plane into four parts known as quadrants denoted by I, II, III and IV. The sign of x and y-coordinates in each of the quadrant is shown below:

#### Distance Formula

The distance between any two points

P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) in the plane is given by,

Also the distance of the point P(x_{1}, y_{1}) from the origin is

#### Section Formula

The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) internally in the ratio m_{1} : m_{2} i.e.,

The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) externally in the ratio, m_{1} : m_{2} i.e., are

(iii) If the ratio in which P divides AB is K : 1, then the coordinates of the point P will be

#### Mid-Point Formula

The coordinates of the mid point P of the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is

#### Area of a Triangle

The area of ∆ABC formed by the vertices A(x_{1}, y_{1}), B(x_{2}, y_{2}) is given by

Note:

(i) Area of triangle = × base × Altitude

(ii) Area of polygon can be calculated by dividing it into the triangular region.

(iii) If three points are collinear then area of the triangle formed by them is zero.

### NCERT Solutions for Class 10 Maths

- Chapter 1 Real Numbers
- Chapter 2 Polynomials
- Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- Chapter 6 Triangles
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

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