MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 28

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCoordinate Geometry

If $Q (0, 1)$ is equidistant from $P (5, - 3)$ and $R (x, 6)$ , find the values of $x$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Equidistant means $QP = QR$ ; square both sides to remove the roots.

Hint 2

After simplifying you get a quadratic in $x$ ; remember it has two 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.

Since Q is equidistant from P and R, $P Q = QR$ , so $P Q^{2} = Q R^{2}$ :
$(5 - 0)^{2} + (- 3 - 1)^{2} = (x - 0)^{2} + (6 - 1)^{2}$
1 mark
$25 + 16 = x^{2} + 25$
1 mark
$x^{2} = 16 \Rightarrow x = 4$ or $x = - 4$
1 mark

Answer: $x = 4$ or $x = - 4$

Where the marks are

Sets up $P Q^{2} = Q R^{2}$ using the distance formula (1 mark)
Simplifies to $41 = x^{2} + 25$ (1 mark)
Obtains $x = 4$ and $x = - 4$ (½ + 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 30/2/1 (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 28

Hints

Step-by-step solution

Revise the chapter

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