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

CBSE Class 10 Mathematics Basic 2023: question 21(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerCoordinate Geometry

Find the coordinates of the point which divides the line segment joining the points $(7, - 1)$ and $(- 3, 4)$ internally in the ratio $2 : 3$ .

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

Hints

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

Hint 1

Use the section formula for internal division in the ratio $m_{1} : m_{2}$ .

Hint 2

Multiply $m_{1}$ with the coordinates of the second point $(- 3, 4)$ and $m_{2}$ with those of the first point $(7, - 1)$ .

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 $P (x, y)$ divide the join of $A (7, - 1)$ and $B (- 3, 4)$ internally in the ratio $m_{1} : m_{2} = 2 : 3$ . By the section formula, $x = \frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}} = \frac{2 ( - 3 ) + 3 ( 7 )}{2 + 3} = \frac{15}{5} = 3$ .
1 mark
$y = \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}} = \frac{2 ( 4 ) + 3 ( - 1 )}{5} = \frac{5}{5} = 1$ . So the required point is $P (3, 1)$ .
1 mark

Answer: (3, 1)

Where the marks are

Applies the section formula correctly to get $x = 3$ (1 mark)
Gets $y = 1$ and states the point $(3, 1)$ (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 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 21(a)

Hints

Step-by-step solution

Revise the chapter

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