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 x1 = 0, y1 = 0, x2 = 36 and y2 = 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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