MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 2 marks · Very short answer

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

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, 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

The line segment joining the points A(4, $- 5$ ) and B(4, 5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

The section formula needs the ratio AP : PB, not AP : AB.

Hint 2

If AP is 2 parts of AB's 5 parts, how many parts is PB?

Hint 3

Use $(\frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}, \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}})$ with ratio 2 : 3.

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.

Since $A P : A B = 2 : 5$ , we get $P B = A B - A P$ , so $A P : P B = 2 : 3$ . Hence P divides AB internally in the ratio $2 : 3$ .
½ mark
By the section formula with $m_{1} = 2, m_{2} = 3$ , A(4, −5), B(4, 5):
$x = \frac{2 ( 4 ) + 3 ( 4 )}{2 + 3} = \frac{8 + 12}{5} = 4$ , and $y = \frac{2 ( 5 ) + 3 ( - 5 )}{5} = \frac{10 - 15}{5} = - 1$ .
1 mark
Therefore the coordinates of P are $(4, - 1)$ .
½ mark

Answer: P(4, −1)

Where the marks are

Converts AP : AB = 2 : 5 into AP : PB = 2 : 3 (½ mark)
Applies the section formula correctly to get x = 4 and y = −1 (1 mark)
States P = (4, −1) (½ 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 30/5/1 (Standard): 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 Standard 2023: question 21(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry