Complete solutions of Ex 7.1 Class 10 Maths Chapter 7 with additional questions and answers from new NCERT syllabus textbook Class 10 Maths.

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.

- 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

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 |

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

**Ex 7.1 Class 10 Maths 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:**

**Ex 7.1 Class 10 Maths Question 2.**

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

**Solution:**

Let the given points be P(0, 0) and Q(36, 15).

Then x_{1} = 0, y_{1} = 0, x_{2} = 36 and y_{2} = 15

**Ex 7.1 Class 10 Maths Question 3.**

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

**Solution:**

Let the given points are A (1, 5), B (2, 3) and C (-2, -11). Then:

Since AB + BC ≠ AC

Hence, the given points are not collinear.

**Ex 7.1 Class 10 Maths Question 4.**

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

**Solution:**

Let the given points be A(5, -2), B (6, 4) and C (7, -2). Then:

Since AB = BC, so the triangle is isosceles.

Hence, the given points are the verticles of an isosceles triangle.

**Ex 7.1 Class 10 Maths 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:

From the figure, let the points along with coordinates be A (3, 4), B (6, 7), C (9, 4) and D (6, 1).

Then by distance formula, we have:

∴ AB = BC = CD = DA \({ 3 }\sqrt { 2 } \)

and diagonals AC = BD = 6

Thus, ABCD is a square and Champa is correct.

**Ex 7.1 Class 10 Maths 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:**

**(i)** Let points be A (-1, -2), B (1, 0), C (-1, 2) and D (-3, 0), Then:

**(ii)** Let points be A (-3, 5), B (3, 1), C (0, 3) and D (-1, -4). Then:

**(iii)** Let points be A(4, 5), B (7, 6), C (4, 3) and D (1, 2). Then:

**Ex 7.1 Class 10 Maths Question 7.**

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

**Solution:**

Let A (2, -5) and B (-2, 9) be the given points.

Also let P (x, 0) be the point on x-axis such that

**Ex 7.1 Class 10 Maths 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:**

Given: PQ = 10 units

**Ex 7.1 Class 10 Maths 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:**

Given that Q(0, 1) is equidistant from P(5, -3) and R(x, 6)

**Ex 7.1 Class 10 Maths 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:**

Let P(x, y) is equidistant from Q(3, 6) and R(-3, 4).

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