Question

Find the area of the triangle formed by the lines: $ y = -4, \quad y = x, \quad y = -4 $

• A. \( 16 \)
• B. \( 8 \)
• C. \( 12 \)
• D. \( 10 \)

Hint:

For calculating the area of a triangle formed by lines, use the formula \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \), where the base and height are the perpendicular distances between the lines and the x-axis.

Answer 1

The Correct Option is B

The three lines given are: 1. \( y = -4 \) (horizontal line at \( y = -4 \)) 2. \( y = x \) (diagonal line) 3. \( y = -4 \) (same as the first one) These lines form a right triangle with the x-axis. - The first and second lines intersect at the point \( (-4, -4) \). 
- The second and third lines intersect at the point \( (4, 4) \). 
Next, we calculate the area of the triangle. The base of the triangle is the distance between the x-axis and the line \( y = -4 \), which is 4 units. The height of the triangle is the distance between the line \( y = x \) and the x-axis, which is also 4 units. 
Thus, the area of the triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8 \] Therefore, the correct answer is (B) \( 8 \).