Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : (–4, 2) Rajasthan High Court Point B : (4, –4) Birla Mandir Point C : (4, 3) Heera Bagh Point D : (–5, –2) Amar Jawan Jyoti Based on the above, answer the following questions : (i) Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ? (ii) There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio. (iii)(a) Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer. (iii)(b) Using section formula, show that points A, O and B are not collinear.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 38

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedCoordinate Geometry

Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below :

Point A : (–4, 2) Rajasthan High Court
Point B : (4, –4) Birla Mandir
Point C : (4, 3) Heera Bagh
Point D : (–5, –2) Amar Jawan Jyoti

Based on the above, answer the following questions :

(i)
Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ?
1 mark
(ii)
There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio.
1 mark
(iii)(a)
Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer.
2 marks
OR
(iii)(b)
Using section formula, show that points A, O and B are not collinear.
2 marks

Figure in the paper: Street map of Jaipur overlaid with X and Y axes through origin O (Rambagh Palace). Marked points: A (Rajasthan High Court) upper left, C (Heerabagh) upper right on positive y side, D (Amar Jawan Jyoti) lower left, B (Birla Mandir, Jaipur) lower right. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

For (i), she travels from C to A and back, so double the distance AC.

Hint 2

A point on the X-axis has y-coordinate 0; use the section formula with ratio k : 1.

Hint 3

For collinearity, find k separately from the x- and y-coordinates and check whether the two values agree.

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.

(i) Rehana goes from C(4, 3) to A(−4, 2) and back, so distance = $2 \times A C$ .
$A C = (- 4 - 4)^{2} + (2 - 3)^{2}$
½ mark
$A C = 64 + 1 = 65$
Distance covered daily $= 265$ units.
½ mark
(ii) Let the point P(x, 0) on the X-axis divide AD in the ratio $k : 1$ , with A(−4, 2) and D(−5, −2).
By the section formula, the y-coordinate gives $0 = \frac{k ( - 2 ) + 1 ( 2 )}{k + 1}$ .
½ mark
$\Rightarrow - 2 k + 2 = 0 \Rightarrow k = 1$
The required ratio is 1 : 1.
½ mark
(iii)(a) Distance of Birla Mandir B(4, −4) from Heera Bagh C(4, 3):
$B C = (4 - 4)^{2} + (- 4 - 3)^{2} = 49 = 7$ units
1 mark
Distance of B from Amar Jawan Jyoti D(−5, −2):
$B D = (4 + 5)^{2} + (- 4 + 2)^{2} = 81 + 4 = 85$ units
Since $B C \neq = B D$ , Birla Mandir is not equidistant from Heera Bagh and Amar Jawan Jyoti.
1 mark
(iii)(b) Suppose A(−4, 2), O(0, 0) and B(4, −4) are collinear, and O divides AB in the ratio $k : 1$ .
½ mark
x-coordinate: $0 = \frac{4 k - 4}{k + 1} \Rightarrow k = 1$
½ mark
y-coordinate: $0 = \frac{- 4 k + 2}{k + 1}$
½ mark
$\Rightarrow k = \frac{1}{2}$
The two values of $k$ are different, so no single ratio works. Hence A, O and B are not collinear.
½ mark

Answer: (i) 2√65 units; (ii) 1 : 1; (iii)(a) No, BC = 7 units but BD = √85 units; (iii)(b) k = 1 from x and k = 1/2 from y, so A, O, B are not collinear

Where the marks are

(i) Uses distance = 2AC with correct substitution in the distance formula (½ mark)
(i) 2√65 units (½ mark)
(ii) Uses the section formula with y-coordinate = 0 (½ mark)
(ii) Ratio 1 : 1 (½ mark)
(iii)(a) BC = 7 units (1 mark)
(iii)(a) BD = √85 units and concludes not equidistant (1 mark)
(iii)(b) Assumes O divides AB in the ratio k : 1 (½ mark)
(iii)(b) k = 1 from the x-coordinate (½ mark)
(iii)(b) Sets up the y-coordinate equation (½ mark)
(iii)(b) k = 1/2, values differ, so not collinear (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Section Formula (Internal Division)

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/4/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2026: question 38

Hints

Step-by-step solution

Revise the chapter

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