MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 31

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerCoordinate Geometry

Find the coordinates of the points of trisection of the line segment joining the points A(5, $- 3$ ) and B( $- 4$ , 3).

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

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

Hint 2

Use $(\frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}, \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}})$ for each point.

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 P and Q be the points of trisection, with $A P : P B = 1 : 2$ . By section formula:
$P (\frac{1 ( - 4 ) + 2 ( 5 )}{1 + 2}, \frac{1 ( 3 ) + 2 ( - 3 )}{1 + 2})$
1 mark
$P = (\frac{6}{3}, \frac{- 3}{3}) = (2, - 1)$
½ mark
Q divides AB with $A Q : QB = 2 : 1$ :
$Q (\frac{2 ( - 4 ) + 1 ( 5 )}{2 + 1}, \frac{2 ( 3 ) + 1 ( - 3 )}{2 + 1})$
1 mark
$Q = (\frac{- 3}{3}, \frac{3}{3}) = (- 1, 1)$
½ mark

Answer: (2, −1) and (−1, 1)

Where the marks are

Section formula for P in ratio 1 : 2 (1 mark)
P = (2, −1) (½ mark)
Section formula for Q in ratio 2 : 1 (1 mark)
Q = (−1, 1) (½ 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 paper2024 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 2024: question 31

Hints

Step-by-step solution

Revise the chapter

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