MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 24

From the official CBSE sample question paper for 2024-25, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerCoordinate Geometry

Find the point(s) on the $x$ -axis which is at a distance of $41$ units from the point $(8, - 5)$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

What is the $y$ -coordinate of every point on the $x$ -axis?

Hint 2

Use the distance formula with $(x, 0)$ and $(8, - 5)$ , set it equal to $41$ and square both sides.

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.

Any point on the $x$ -axis has $y$ -coordinate 0, so let the required point be $P (x, 0)$ .
½ mark
By the distance formula, the distance from $(8, - 5)$ is $(8 - x)^{2} + (- 5 - 0)^{2} = 41$ , that is, $(8 - x)^{2} + 25 = 41$ .
½ mark
Squaring both sides: $(8 - x)^{2} + 25 = 41 \Rightarrow (8 - x)^{2} = 16 \Rightarrow 8 - x = \pm 4$ .
So $x = 8 - 4 = 4$ or $x = 8 + 4 = 12$ . The required points are $(4, 0)$ and $(12, 0)$ .
1 mark

Answer: $(4, 0)$ and $(12, 0)$

Where the marks are

Takes the point on the $x$ -axis as $(x, 0)$ (½ mark)
Sets up the distance equation correctly (½ mark)
Solves to get both points $(4, 0)$ and $(12, 0)$ (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Distance Formula

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2024-25: question 24

Hints

Step-by-step solution

Revise the chapter

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