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

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 21(B)

From the official CBSE sample question paper for 2024-25, 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

In the given figure, $△ A B C$ is an equilateral triangle. Coordinates of vertices A and B are $(0, 3)$ and $(0, - 3)$ respectively. Find the coordinates of points C.

Figure in the paper: Coordinate axes with X'OX horizontal and YOY' vertical. A is on the positive Y-axis at (0,3), B is on the negative Y-axis at (0,-3). C lies on the positive X-axis, forming equilateral triangle ABC with AB as the base on the Y-axis. See it in the official paper.

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

All sides of an equilateral triangle are equal, so find $A B$ first.

Hint 2

Triangle $A O C$ is right-angled at $O$ . Use Pythagoras to find $O C$ .

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.

$A B = 3 - (- 3) = 6$ units. Since $△ A B C$ is equilateral, $A C = A B = 6$ units.
½ mark
$C$ lies on the positive x-axis, so the origin $O$ is the midpoint of $A B$ and $O A = 3$ .
In right $△ A O C$ : $O C = A C^{2} - O A^{2} = 36 - 9 = 27 = 33$ units.
1 mark
Hence the coordinates of C are $(33, 0)$ .
½ mark

Answer: $C (33, 0)$

Where the marks are

Finds $A B = A C = 6$ (½ mark)
Uses Pythagoras to get $O C = 33$ (1 mark)
States $C = (33, 0)$ (½ mark)

Revise the chapter

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

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 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 21(B)

Hints

Step-by-step solution

Revise the chapter

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