MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 21(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

If $A (1, 1)$ and $B (7, 9)$ are the end points of a diameter of a circle, then find the co-ordinates of the centre of the circle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Where does the centre lie on a diameter?

Hint 2

The centre is the mid-point of AB: average the x-coordinates and average the y-coordinates.

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.

The centre of a circle is the mid-point of any diameter. By the mid-point formula, centre $= (\frac{1 + 7}{2}, \frac{1 + 9}{2})$
1 mark
$= (\frac{8}{2}, \frac{10}{2}) = (4, 5)$
1 mark

Answer: Centre is $(4, 5)$

Where the marks are

Uses the mid-point formula with the end points of the diameter (1 mark)
Gets the centre $(4, 5)$ (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Midpoint Formula and Points of Trisection

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 430/3/1 (Basic): 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 Basic 2024: question 21(b)

Hints

Step-by-step solution

Revise the chapter

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