NCERT Maths Solution Class-10
Coordinate geometry
Coordinate geometry
Exercise -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)
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.
sol.
Question 3:
Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.
Sol.
Question 4:
Check whether (5, − 2), (6, 4) and (7, − 2) are the vertices of an isosceles triangle.
Sol.
Question 5:
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the 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.
Sol.
Therefore, ABCD is a square and hence, Champa was 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)
Sol.
Question 7:
Find the point on the x-axis which is equidistant from (2, − 5) and (−2, 9).
Sol.
Find the point on the x-axis which is equidistant from (2, − 5) and (−2, 9).
We have to find a point on x-axis. Therefore, its y-coordinate will be 0.Let the point on x-axis P be (x,0).
Question 8
Therefore, the point is (− 7, 0).
Find the values of y for which the distance between the points P(2,−3) and Q (10, y) is 10 units.
Sol.
Question 9:
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Sol.
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).
Point (x, y) is equidistant from (3, 6) and (−3, 4).
Sol.
