Area of Triangle Formed by Three Lines

Video Explanation

Question

Find the area of the triangle formed by the lines \(x = 3\), \(y = 4\), and \(x = y\).

Solution

Step 1: Find Points of Intersection

Intersection of \(x = 3\) and \(y = 4\):

\[ (3, 4) \]

Intersection of \(x = 3\) and \(x = y\):

\[ y = 3 \Rightarrow (3, 3) \]

Intersection of \(y = 4\) and \(x = y\):

\[ x = 4 \Rightarrow (4, 4) \]

Step 2: Vertices of Triangle

\[ (3,4),\ (3,3),\ (4,4) \]

Step 3: Apply Area Formula

This is a right-angled triangle:

Base = 1 (from 3 to 4), Height = 1 (from 3 to 4)

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

Final Answer

\[ \text{Area} = \frac{1}{2} \text{ sq. unit} \]