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Class 10 RD Sharma Solutions- Chapter 14 Coordinate Geometry – Exercise 14.1
  • Last Updated : 02 Feb, 2021

Problem 1: On which axis do the following points lie?

(i) P (5, 0)

Solution:

As its ordinate is 0. So, it lies on x-axis.

(ii) Q (0, -2)

Solution:



As its abscissa is 0. So, it lies on y-axis (negative half).

(iii) R (-4, 0)

Solution:

As its ordinate is 0. So, it lies on x-axis (negative half).

(iv) S (0, 5)

Solution:

As its abscissa is 0. So, it lies on y-axis.

Problem 2: Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when –

(i) A coincides with the origin and AB and AB and coordinate axes are parallel to the sides AB and AD respectively.

(ii) The center of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.

Solution: 



(I)

(II)

(i) Coordinate of the vertices of the square ABCD of side 2a will be – A(0, 0), B(2a, 0), C(2a, 2a) and D(0, 2a)

(ii) Coordinate of the vertices of the square ABCD of side 2a will be – A(a, a), B(-a, a), C(-a, -a) and D(a, -a)

Problem 3: The base PQ of two equilateral triangles PQR and PQR’ with side 2a lies along y- axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R’ of the triangles.

Solution:

Here, We have two equilateral triangles PQR and PQR’ with side 2a lying along y-axis.

O is the mid-point of PQ.

Now, in ∆QOR, ∠QOR = 90°

Now, By using Pythagoras theorem – 

OR2 + OQ2 = QR2

OR2 = (2a)2 – (a)2  

OR2 = 3a2

OR = (√3)a

Thus, the coordinate of vertex R is (√3 a, 0) and coordinate of vertex R’ is (-√3 a, 0)

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