Determine graphically, the coordinates of vertices of a triangle whose equations are $2x - 3y + 6 = 0$; $2x + 3y - 18 = 0$ and $x = 0$. Also, find the area of this triangle.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
Step 1 – Find points for each line:
Line 1: $2x - 3y + 6 = 0$
| x | 0 | 3 |
|---|---|---|
| y | 2 | 4 |
Line 2: $2x + 3y - 18 = 0$
| x | 0 | 9 |
|---|---|---|
| y | 6 | 0 |
Line 3: $x = 0$ (the y-axis)
Step 2 – Plot and draw all three lines on graph paper.
Step 3 – Read the vertices (intersection points):
- Line 1 and Line 3 ($x=0$): Put $x=0$ in Line 1 → $y=2$. Vertex A = (0, 2)
- Line 2 and Line 3 ($x=0$): Put $x=0$ in Line 2 → $y=6$. Vertex B = (0, 6)
- Line 1 and Line 2: Adding both equations → $4x - 12 = 0$ → $x = 3$, $y = 4$. Vertex C = (3, 4)
Step 4 – Area of triangle:
Base AB lies on y-axis: $AB = 6 - 2 = 4$ units.
Height = perpendicular distance from C(3, 4) to y-axis $= 3$ units.
$$\text{Area} = \frac{1}{2} \times 4 \times 3 = \boxed{6 \text{ sq. units}}$$
Source: Chapter 3, Section 3.2 – Graphical Method of Solution
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Explanation
- Graphical method: plot 2 points per line, draw the lines, and read intersection coordinates.
- Three vertices come from the three pairwise intersections of the three lines.
- Area shortcut: when two vertices share the y-axis, use them as base; the x-coordinate of the third vertex directly gives the height — avoids the coordinate-geometry formula and is faster in board exams.
- Examiners award marks for: the correct table of values (1 mark), correctly drawn graph (1 mark), correct vertices (2 marks), and correct area (1 mark).