NCERT10th MathematicsExercise 7.1Topic: 7 Coordinate geometry
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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)
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:
from the point (3, 6) and (– 3, 4).
Solution:
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