CBSE Class 10 Mathematics Standard sample paper 2023-24: question 7
From the official CBSE sample question paper for 2023-24, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.
Q7 · 1 mark · MCQCoordinate Geometry
A point is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
- (A)0
- (B)1
- (C)2
- (D)infinitely many
Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.
Hints
Open one hint at a time and try again before the next.
Hint 1
What shape is formed by all points 5 units from the origin?
Hint 2
How many points lie on an arc of a circle?
Step-by-step solution
Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.
Distance 5 from the origin means . This is a circle of radius 5 centred at the origin.
- 1 mark
Part of this circle (an arc) lies in the third quadrant, where . An arc contains infinitely many points. Option (D).
Answer: infinitely many, option (D)
Where the marks are
- Recognises the locus as a circle whose third-quadrant arc has infinitely many points, option (D) (1 mark)
Revise the chapter
- Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
- Topic: Distance Formula
More questions from Coordinate Geometry
- 2023 board paper, set 30/2/1 (Standard), Q23 · 2 marksShow that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle.
- 2023 board paper, set 30/2/1 (Standard), Q28 · 3 marksIf Q(0, 1) is equidistant from P(5, -3) and R(x, 6), find the values of x.
- 2023 board paper, set 30/5/1 (Standard), Q21(b) · 2 marksPoint P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that x = y.
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