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.

• 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

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:
Let the given points be P(0, 0) and Q(36, 15).
Then x₁ = 0, y₁ = 0, x₂ = 36 and y₂ = 15

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.

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.

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
and diagonals AC = BD = 6
Thus, ABCD is a square and Champa is correct.

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:

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

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

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)

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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