170-NCERT-10-7-Coordinate geometry - Ex- 7.1

NCERT

10th Mathematics

Exercise 7.1

Topic: 7 Coordinate geometry

Click here for ⇨ NCERT-10-6-Triangles - Ex- 6.6

EXERCISE 7.1

Q 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:

Q2. 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.

Solution:

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

Solution:

Q 4. Check whether (5, – 2), (6, 4), and (7, – 2) are the vertices of an isosceles

triangle.

Solution:

Q 5. In a classroom, 4 friends are seated at points A, B, C, and D as shown

in following 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 the distance formula, find which of them is correct.

Solution:

1) First we will find the coordinates of points A, B, C, and D, See the following

figure.

Q 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) (– 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)

Q 7. Find the point on the x-axis which is equidistant from (2, –5) 

and (–2, 9).

Solution:

Q 8. Find the values of y for which the distance between the points 

P(2, – 3) and Q(10, y) is 10 units.

Solution:

Q 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:

Q 10. Find a relation between x and y such that the point (x, y) is equidistant

from the point (3, 6) and (– 3, 4).

Solution:

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Click here for ⇨ NCERT-10-7-Coordinate-geometry - Ex- 7.2

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