MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2025: question 38

Set in the CBSE Class 10 board exam of 2025, 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: A rectangle ABCD with A(10, 10) at bottom left, B(40, 10) at bottom right, C(40, 50) at top right and D(x, y) at top left. Diagonals AC and DB intersect at E at the centre. Arrows show Anita's path from A along diagonal AC to E, then from E along diagonal EB to B, then from B back to A along BA. Anil's path runs along the boundary from C via D to A. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 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, so their intersection point is the mid-point of each diagonal.

Hint 2

Use the mid-point formula $(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$ and the distance formula $(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ .

Hint 3

For D, equate the mid-point of BD to E. For Anita, add the three lengths AE, EB and BA.

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) By the distance formula:
$B C = (40 - 40)^{2} + (50 - 10)^{2} = 0 + 1600 = 40$ units
1 mark
(iii)(a) E is also the mid-point of BD:
$(\frac{x + 40}{2}, \frac{y + 10}{2}) = (25, 30)$
This gives $x + 40 = 50 \Rightarrow x = 10$ and $y + 10 = 60 \Rightarrow y = 50$ . 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) Anita's distance $= A E + E B + B A$ :
$A E = (25 - 10)^{2} + (30 - 10)^{2} = 225 + 400 = 25$
$E B = (40 - 25)^{2} + (10 - 30)^{2} = 225 + 400 = 25$
$B A = (10 - 40)^{2} + 0^{2} = 30$
1½ marks
(iii)(b) Total distance $= 25 + 25 + 30 = 80$ units
½ mark

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

Where the marks are

(i) E as the mid-point of AC gives (25, 30) (1 mark)
(ii) Distance formula gives BC = 40 (1 mark)
(iii)(a) Uses E as the mid-point of BD to get D(10, 50) (½ + ½ marks)
(iii)(a) BD = 50 units (1 mark)
(iii)(b) Finds AE = 25, EB = 25 and BA = 30 (1½ marks)
(iii)(b) Total distance = 80 units (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 paper2025 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 2025: question 38

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry