MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 29(b)

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, section C, question 29(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(b) · 3 marks · Short answerCoordinate Geometry

In the given figure, in $△ A B C$ points D and E are mid-points of sides BC and AC respectively. If given vertices are A(4, -2), B(2, -2) and C(-6, -7), then verify the result $D E = \frac{1}{2} A B$ .

Figure in the paper: Triangle ABC with B at upper left, A at upper right (AB horizontal on top), and C at lower left. D is the midpoint of BC and E is the midpoint of AC; the segment DE is drawn horizontally joining D and E. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/5/1.

Hints

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

Hint 1

Use the mid-point formula to locate D and E.

Hint 2

Then use the distance formula for DE and for AB and compare.

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.

D is the mid-point of BC: $D = (\frac{2 + ( - 6 )}{2}, \frac{- 2 + ( - 7 )}{2}) = (- 2, - \frac{9}{2})$
1 mark
E is the mid-point of AC: $E = (\frac{4 + ( - 6 )}{2}, \frac{- 2 + ( - 7 )}{2}) = (- 1, - \frac{9}{2})$
1 mark
$D E = (- 1 + 2)^{2} + (- \frac{9}{2} + \frac{9}{2})^{2} = 1^{2} + 0^{2} = 1$ and $A B = (4 - 2)^{2} + (- 2 + 2)^{2} = 2^{2} + 0^{2} = 2$
1 mark
Hence $D E = 1 = \frac{1}{2} \times 2 = \frac{1}{2} A B$ . Verified.

Answer: DE = 1, AB = 2, so DE = ½ AB (verified)

Where the marks are

Finds D $= (- 2, - \frac{9}{2})$ (1 mark)
Finds E $= (- 1, - \frac{9}{2})$ (1 mark)
DE = 1 and AB = 2 giving DE = ½AB (½ + ½ marks)

Revise the chapter

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

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 430/5/1 (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 29(b)

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry