Q.5 (ii) Draw the graph of the equation \(x + y = 4\) and answer the following questions :
(a) Which type of triangle is formed by the line with X and Y-axes based on its sides.
(b) Find the area of that triangle.
Best answer
Answer: (a) an isosceles right-angled triangle (b) 8 square units
\(x + y = 4 \Rightarrow y = 4 - x\)
| \(x\) | 0 | 4 | 2 |
| \(y\) | 4 | 0 | 2 |
| \((x, y)\) | (0, 4) | (4, 0) | (2, 2) |
Graph (to be drawn on graph paper): Scale: on both axes 1 cm = 1 unit. Draw the X-axis and Y-axis through the origin O. Plot A(0, 4), B(2, 2) and C(4, 0) and join them with a straight line labelled \(x + y = 4\). The line meets the Y-axis at A(0, 4) and the X-axis at C(4, 0), so it forms \(\triangle AOC\) with the axes (shade it).
(a) OA = 4 units and OC = 4 units, and \(\angle AOC = 90^\circ\) (the axes are perpendicular). Two sides are equal and one angle is a right angle, so \(\triangle AOC\) is an isosceles right-angled triangle.
(b) Area of \(\triangle AOC = \dfrac12 \times OC \times OA = \dfrac12 \times 4 \times 4 = 8\) square units.
(Note: a picture of the graph cannot be shown here; in the examination the graph itself must be drawn as described above.)
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