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

CBSE Class 10 Mathematics Basic 2023: question 23(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/2/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(a) · 2 marks · Very short answerCoordinate Geometry

Find the value(s) of 'x' so that $P Q = QR$ , where the coordinates of P, Q and R are $(6, - 1)$ , $(1, 3)$ and $(x, 8)$ respectively.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/2/1.

Hints

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

Hint 1

Use the distance formula $(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ for PQ and QR.

Hint 2

Square both sides to remove the roots, then solve for $(x - 1)^{2}$ . Remember both signs of the square root.

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.

Using the distance formula, $P Q = QR$ gives $(6 - 1)^{2} + (- 1 - 3)^{2} = (x - 1)^{2} + (8 - 3)^{2}$
1 mark
Squaring: $25 + 16 = (x - 1)^{2} + 25 \Rightarrow (x - 1)^{2} = 16 \Rightarrow x - 1 = \pm 4$
½ mark
$x = 5$ or $x = - 3$
½ mark

Answer: x = 5 or x = −3

Where the marks are

Sets up PQ = QR with the distance formula (1 mark)
Simplifies to $(x - 1)^{2} = 16$ (1/2 mark)
Gets $x = 5$ or $- 3$ (1/2 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 430/2/1 (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 23(a)

Hints

Step-by-step solution

Revise the chapter

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