MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2023: question 36

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedCoordinate Geometry

Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle. One such campaign board made by class X student of the school is shown in the figure.

Based on the above information, answer the following questions:

(i)
Find the coordinates of the point of intersection of diagonals AC and BD.
1 mark
(ii)
Find the length of the diagonal AC.
1 mark
(iii)(a)
Find the area of the campaign Board ABCD.
2 marks
OR
(iii)(b)
Find the ratio of the length of side AB to the length of the diagonal AC.
2 marks

Figure in the paper: Coordinate axes with X' on the left and Y upwards. A rectangle ABCD with A(1, 1) at bottom-left, B(7, 1) at bottom-right, C(7, 5) at top-right and D(1, 5) at top-left. The text 'BAN PUBG & SAVE KIDS' is written inside the rectangle. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

The diagonals of a rectangle bisect each other. Where do they meet?

Hint 2

Use the distance formula $(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ for any side or diagonal.

Hint 3

Area of a rectangle is length × breadth. For the ratio, simplify $\frac{6}{2 13}$ .

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 they meet at the midpoint of AC.
Midpoint $= (\frac{1 + 7}{2}, \frac{1 + 5}{2}) = (4, 3)$
1 mark
(ii) $A C = (7 - 1)^{2} + (5 - 1)^{2} = 36 + 16 = 52 = 213$ units
1 mark
(iii)(a) $A B = (7 - 1)^{2} + (1 - 1)^{2} = 6$ units
½ mark
(iii)(a) $B C = (7 - 7)^{2} + (5 - 1)^{2} = 4$ units
½ mark
(iii)(a) Area of ABCD $= A B \times B C = 6 \times 4 = 24$ sq. units
1 mark
(iii)(b) $A B = (7 - 1)^{2} + (1 - 1)^{2} = 6$ units
1 mark
(iii)(b) $\frac{A B}{A C} = \frac{6}{2 13} = \frac{3}{13}$
So the required ratio is $3 : 13$ .
1 mark

Answer: (i) (4, 3); (ii) 2√13 units; (iii)(a) 24 sq. units; (iii)(b) 3 : √13

Where the marks are

(i) Uses the midpoint of AC to get (4, 3) (1 mark)
(ii) Distance formula gives AC = 2√13 (1 mark)
(iii)(a) AB = 6 and BC = 4 (½ + ½ marks)
(iii)(a) Area = 24 sq. units (1 mark)
(iii)(b) AB = 6 (1 mark)
(iii)(b) Ratio AB : AC = 3 : √13 (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Applications of the 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 paper2023 board paper, set 430/4/1 (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 2023: question 36

Hints

Step-by-step solution

Revise the chapter

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