MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 22(A)

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section B, question 22(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(A) · 2 marks · Very short answerCoordinate Geometry

Find the coordinates of the point which divides the join of $A (- 1, 7)$ and $B (4, - 3)$ in the ratio $2 : 3$ .

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

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

Hint 2

Here $m_{1} = 2$ goes with B's coordinates and $m_{2} = 3$ with A's.

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.

By the section formula with $m_{1} : m_{2} = 2 : 3$ , $A (- 1, 7)$ , $B (4, - 3)$ : $x = \frac{2 ( 4 ) + 3 ( - 1 )}{2 + 3} = \frac{8 - 3}{5} = 1$
1 mark
$y = \frac{2 ( - 3 ) + 3 ( 7 )}{2 + 3} = \frac{- 6 + 21}{5} = 3$ . Required point is $(1, 3)$ .
1 mark

Answer: (1, 3)

Where the marks are

Correct x-coordinate 1 using section formula (1 mark)
Correct y-coordinate 3 (1 mark)

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 paper2023 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 22(A)

Hints

Step-by-step solution

Revise the chapter

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