Let distance between two points A(x 1 , y 1 ) and B(x 2 ,y …

Maths Rectangular Cartesian Co-ordinates Mix Single Correct MCQ

Published on: August 14, 2026

Let distance between two points A(x 1 , y 1 ) and B(x 2 ,y 2 ) be denoted by d(A, B) and d(A, B) = max.{|x 2 – x 1 |, |y 2 – y 1 | }

(i) If O is origin and P(x, y) is a point on line y = then d(OP) is equal to –

y, y ∈ R 64 sq. units 1

x, x ∈ R 54 sq. units 2

x, x < 0 16 sq. units

y, y ≥ 0 (ii) Area of region bounded by locus of point P satisfying d(P, C) = 4 where C is (1, 2) is- 32 sq. units (iii) Distance between P(3, 4) and Q(4, 2) is- None

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Ans.

(i)

Sol. d(O,P) = max. {|x|, |y|}

= max. {|x|, √ 3 |x|}

= √ 3 |x| = y where y ≥ 0

(ii)

Sol. Now d(P,C) = max. {| x – 1|, | y – 2| } = 4

Case 1 : | x – 1 |= 4 so | y – 2 | ≤ 4

x = –3, 5 –2 ≤ y ≤ 6

Case 2 :

| y – 2 | = 4 so | x – 1| ≤ 4

y = –2, 6 –3 ≤ x ≤ 5

∴ Area = 8 × 8 = 64

(iii)

Sol. d(P,Q) = max. {| 1 |, | 2 | } = 2

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