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

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

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, 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

Find the value(s) of y for which the distance between the points $A (3, - 1)$ and $B (11, y)$ is 10 units.

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

Write $A B^{2} = 100$ using the distance formula.

Hint 2

After simplifying, $(y + 1)^{2}$ equals a perfect square; remember both the positive and negative square roots.

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.

By the distance formula, $A B^{2} = (11 - 3)^{2} + (y + 1)^{2}$ . Since $A B = 10$ , $64 + (y + 1)^{2} = 100$ .
1 mark
$(y + 1)^{2} = 36 \Rightarrow y + 1 = \pm 6$ .
$y = 6 - 1 = 5$ or $y = - 6 - 1 = - 7$ .
1 mark

Answer: y = 5 or y = −7

Where the marks are

Forms the equation $(11 - 3)^{2} + (y + 1)^{2} = 100$ (1 mark)
Obtains $y = 5$ (½ mark) and $y = - 7$ (½ 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 paper2023 board paper, set 430/1/1 (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 2023: question 21(b)

Hints

Step-by-step solution

Revise the chapter

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