Area of Triangle Formed by Line with Axes

Video Explanation

Question

Find the area of the triangle formed by the line \(\frac{x}{a} + \frac{y}{b} = 1\) with the coordinate axes.

Solution

Step 1: Identify Intercepts

Given equation:

\[ \frac{x}{a} + \frac{y}{b} = 1 \]

x-intercept: \( (a, 0) \)

y-intercept: \( (0, b) \)

Step 2: Form Triangle

The triangle is formed with vertices:

\[ (0,0),\ (a,0),\ (0,b) \]

Step 3: Apply Area Formula

Area of triangle:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

\[ = \frac{1}{2} \times a \times b \]

Final Answer

\[ \text{Area} = \frac{1}{2} ab \]