Exercise 7.1 (NCERT) – Coordinate Geometry, Class 10
| Chapter 7 | Exercise 7.1 | Class 10 |
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Below are the Quick links for all questions of Exercise 7.1, Coordinate Geometry, Class 10. Click a link to view the solution of corresponding question.
Below are the solutions of every question of exercise 7.1 of chapter 7, Coordinate Geometry, NCERT of class 10. YouTube video tutorial of every question is also embedded along with the written solution.
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)
Complete Chapter – Video Tutorial
Question 2
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
The problem given in section 7.2 has the same solution. Watch the video to know more about it.
Question 3
Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.
Question 4
Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Since two sides are equal, the triangle is isosceles.
Question 5
In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. 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.
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)
All sides are equal.
Now, checking the diagonals:
Diagonals are also equal.
Hence it is square.
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Now, checking the diagonals:
Since opposite sides are equal, and the diagonals are not equal, the quadrilateral is a parallelogram.
Question 7
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Question 8
Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 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.
Question 10
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).