MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2026: question 38

Set in the CBSE Class 10 board exam of 2026, paper 430/2/1, 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

A field is in the form of a rectangle. The coordinates of the rectangular field ABCD are A(10, 10), B(40, 10), C(40, 50) and D(x, y). Anil and Anita, two friends decided to have a race. Anita started from point A and moved to point E along the diagonal AC, where E is the point of intersection of both the diagonals of ABCD. From point E, she moved to point B along the other diagonal DB and then moved back to point A along BA. While Anil started from point C and ran to point A via D along the boundary of the field.

Based on the above information, answer the following questions :

(i)
Find the coordinates of point E.
1 mark
(ii)
Find the distance between the points B and C.
1 mark
(iii)
(a) Find the coordinates of point D and the distance BD.
2 marks
OR
(iii)
(b) Find the total distance travelled by Anita.
2 marks

Figure in the paper: Rectangle ABCD with A(10, 10) bottom-left, B(40, 10) bottom-right, C(40, 50) top-right, D(x, y) top-left. Diagonals AC and DB intersect at E. Arrows mark Anita's path A to E along AC, E to B along DB, and B to A along BA; Anil's path runs C to D to A along the boundary. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

The diagonals of a rectangle bisect each other.

Hint 2

Use the mid-point formula for E, and then for D using E and B.

Hint 3

Anita's path is half of AC, plus half of BD, plus AB.

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) The diagonals of a rectangle bisect each other, so E is the mid-point of AC: $E = (\frac{10 + 40}{2}, \frac{10 + 50}{2}) = (25, 30)$ .
1 mark
(ii) $B C = (40 - 40)^{2} + (50 - 10)^{2} = 1600 = 40$ units.
1 mark
(iii)(a) E is also the mid-point of BD: $\frac{40 + x}{2} = 25 \Rightarrow x = 10$ and $\frac{10 + y}{2} = 30 \Rightarrow y = 50$ . So $D = (10, 50)$ .
1 mark
(iii)(a) $B D = (10 - 40)^{2} + (50 - 10)^{2} = 900 + 1600 = 2500 = 50$ units.
1 mark
(iii)(b) $A C = 3 0^{2} + 4 0^{2} = 50$ , so $A E = 25$ . Also $E B = \frac{B D}{2} = 25$ and $B A = 40 - 10 = 30$ . Total distance travelled by Anita $= 25 + 25 + 30 = 80$ units.
2 marks

Answer: (i) E(25, 30); (ii) 40 units; (iii)(a) D(10, 50), BD = 50 units; (iii)(b) 80 units

Where the marks are

(i) Uses the mid-point of AC to get E(25, 30) (1 mark)
(ii) Uses the distance formula to get BC = 40 (1 mark)
(iii)(a) Uses E as the mid-point of BD to get D(10, 50) (1 mark)
(iii)(a) Finds BD = 50 (1 mark)
(iii)(b) Finds AE = 25, EB = 25, BA = 30 and adds them to get 80 (2 marks)

Revise the chapter

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

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 430/2/1 (Basic): 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 Basic 2026: question 38

Hints

Step-by-step solution

Revise the chapter

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