MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 29

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCoordinate Geometry

Find the co-ordinates of the points of trisection of the line-segment joining the points (5, 3) and (4, 5).

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Points of trisection divide the segment in ratios 1 : 2 and 2 : 1.

Hint 2

Use the section formula $(\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})$ .

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.

Let A(5, 3) and B(4, 5), and let C and D be the points of trisection, so C divides AB in the ratio 1 : 2.
½ mark
By section formula: $C (\frac{1 \times 4 + 2 \times 5}{1 + 2}, \frac{1 \times 5 + 2 \times 3}{1 + 2}) = C (\frac{14}{3}, \frac{11}{3})$
1 mark
D divides AB in the ratio 2 : 1.
½ mark
$D (\frac{2 \times 4 + 1 \times 5}{2 + 1}, \frac{2 \times 5 + 1 \times 3}{2 + 1}) = D (\frac{13}{3}, \frac{13}{3})$
1 mark

Answer: $(\frac{14}{3}, \frac{11}{3})$ and $(\frac{13}{3}, \frac{13}{3})$

Where the marks are

Ratio 1 : 2 for first point (½ mark)
First point (14/3, 11/3) (1 mark)
Ratio 2 : 1 for second point (½ mark)
Second point (13/3, 13/3) (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Finding the Ratio and Unknowns with Section 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 430/6/1 (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

Hints

Step-by-step solution

Revise the chapter

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