MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 32

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section D, question 32, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32 · 5 marks · Long answerPair of Linear Equations in Two Variables

Determine graphically, the coordinates of vertices of a triangle whose equations are $2 x - 3 y + 6 = 0$ ; $2 x + 3 y - 18 = 0$ and $x = 0$ . Also, find the area of this triangle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

Make a table of at least two or three points for each line. Choosing x = 0 and x = 3 works nicely.

Hint 2

The line x = 0 is the y-axis. Look where the other two lines cut it and where they cut each other.

Hint 3

Use the side on the y-axis as the base. The height is the x-coordinate of the third vertex.

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.

Line 1: $2 x - 3 y + 6 = 0$ , i.e. $y = \frac{2 x + 6}{3}$ .
x 0 3 −3
y 2 4 0
Plot (0, 2), (3, 4), (−3, 0) and join them to draw the line.
1 mark
Line 2: $2 x + 3 y - 18 = 0$ , i.e. $y = \frac{18 - 2 x}{3}$ .
x 0 3 9
y 6 4 0
Plot (0, 6), (3, 4), (9, 0) and join them to draw the line.
1 mark
Line 3: $x = 0$ is the y-axis itself. Mark it as one side of the triangle.
½ mark
From the graph:
- Line 1 meets the y-axis at A(0, 2).
- Line 1 and line 2 intersect at B(3, 4).
- Line 2 meets the y-axis at C(0, 6).
So the vertices of the triangle are A(0, 2), B(3, 4) and C(0, 6).
1½ marks
Take base AC on the y-axis: $A C = 6 - 2 = 4$ units.
Height = perpendicular distance of B from the y-axis = 3 units.
Area of $△ A B C = \frac{1}{2} \times 4 \times 3 = 6$ sq. units.
1 mark

x	0	3	−3
y	2	4	0

x	0	3	9
y	6	4	0

Answer: Vertices A(0, 2), B(3, 4), C(0, 6); area = 6 sq. units

Where the marks are

Correct table and graph of $2 x - 3 y + 6 = 0$ (1 mark)
Correct table and graph of $2 x + 3 y - 18 = 0$ (1 mark)
Shows $x = 0$ as the y-axis (½ mark)
Reads the vertices (0, 2), (3, 4), (0, 6) from the graph (1½ marks)
Finds area = ½ × 4 × 3 = 6 sq. units (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 32

Hints

Step-by-step solution

Revise the chapter

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