Straight Lines
Area of Triangle
Grade 11
Question:
<p>The area of triangle PAB where P lies on the line <p>x + y = 3</p>, and A and B are the intercepts of another line with the axes, is given. Find the area of triangle PAB if <p>|PA| = |PB| = 2</p>.</p>
Step-by-Step Solution
Key Concept: Use the distance formula and the isosceles triangle property to calculate the area.
<p><strong>Step 1:</strong> Given that P is at <p>(0, 3)</p> on the line <p>x + y = 3</p>.</p><p><strong>Step 2:</strong> If A and B are such that <p>|PA| = |PB| = 2</p>, triangle PAB is isosceles.</p><p><strong>Step 3:</strong> The base AB can be found from the geometry. With a perpendicular distance from P, the area is:</p><p>\[\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 2 = 2\]</p><p>∴ Area of <p>\triangle PAB = 2</p>.</p>
Correct Answer: 2