MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 4

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQCoordinate Geometry

In what ratio, does $x$ -axis divide the line segment joining the points $A (3, 6)$ and $B (- 12, - 3)$ ?

(A)1 : 2
(B)1 : 4
(C)4 : 1
(D)2 : 1

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

Hints

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

Hint 1

A point on the $x$ -axis has $y = 0$ .

Hint 2

Take the ratio as $k : 1$ and put the $y$ -coordinate from the section formula equal to 0.

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 the $x$ -axis divide AB in the ratio $k : 1$ . Any point on the $x$ -axis has $y$ -coordinate 0.
By the section formula, $y = \frac{k ( - 3 ) + 1 ( 6 )}{k + 1} = 0 \Rightarrow - 3 k + 6 = 0 \Rightarrow k = 2$ .
So the ratio is $2 : 1$ . Option (D).
1 mark

Answer: 2 : 1, option (D)

Where the marks are

Uses the section formula with $y = 0$ and gets ratio $2 : 1$ , option (D) (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 30/1/1 (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 4

Hints

Step-by-step solution

Revise the chapter

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