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

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:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 1
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 2

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 x1 = 0, y1 = 0, x2 = 36 and y2 = 15
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 3

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:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 4
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:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 5
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.
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 6
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:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 7
∴    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:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 8

(ii) Let points be A (-3, 5), B (3, 1), C (0, 3) and D (-1, -4). Then:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 9

(iii) Let points be A(4, 5), B (7, 6), C (4, 3) and D (1, 2). Then:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 10

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
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 11

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
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 12

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)
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 13

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).
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 14
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry 15

 

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