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

CBSE Class 10 Mathematics Basic 2024: question 28

Set in the CBSE Class 10 board exam of 2024, paper 430/1/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCoordinate Geometry

Find the co-ordinates of the points of trisection of the line segment joining the points $(- 2, 2)$ and $(7, - 4)$ .

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

Hints

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

Hint 1

Points of trisection divide the segment into three equal parts, i.e. in ratios 1:2 and 2:1.

Hint 2

Apply the section formula once for each ratio.

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 $A (- 2, 2)$ , $B (7, - 4)$ and let P, Q be the points of trisection, so $A P : P B = 1 : 2$ and $A Q : QB = 2 : 1$ . Section formula: $(\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})$ .
P (1:2): $(\frac{1 ( 7 ) + 2 ( - 2 )}{3}, \frac{1 ( - 4 ) + 2 ( 2 )}{3}) = (\frac{3}{3}, \frac{0}{3}) = (1, 0)$
1½ marks
Q (2:1): $(\frac{2 ( 7 ) + 1 ( - 2 )}{3}, \frac{2 ( - 4 ) + 1 ( 2 )}{3}) = (\frac{12}{3}, \frac{- 6}{3}) = (4, - 2)$
1½ marks

Answer: $(1, 0)$ and $(4, - 2)$

Where the marks are

Uses ratio 1:2 with section formula and gets $P (1, 0)$ (1½ marks)
Uses ratio 2:1 and gets $Q (4, - 2)$ (1½ marks)

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 paper2024 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 28

Hints

Step-by-step solution

Revise the chapter

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