The area of the triangle formed by the line 2x - 4y – 7 = 0 with the coordinate axis is:

Correct option is D

Given:

The equation of the line is:

2x−4y−7=0

Formula Used:

A line intersects the x-axis when y=0 and the y-axis when x=0.
The area of a triangle formed by the x-axis and y-axis is given by:

​$$\text{Area} = \frac{1}{2} \times \text{Intercept on x-axis} \times \text{Intercept on y-axis}$$​​

Solution:

Find x-intercept

Set y=0 in the equation:

2x - 4(0) - 7 = 0

x =$$\frac{7}{2}$$​​

So, x-intercept =$$\left(\frac{7}{2}, 0\right)$$​​

Find y-intercept

Set x=0 in the equation:

2(0)−4y−7=0

y = -$$\frac{7}{4}$$​​

So, y-intercept = $$\left(0, -\frac{7}{4}\right)$$

Since we take absolute values for area calculations, we use 74\frac{7}{4}
​$$\frac{7}{4}$$​​​

​$$\text{Area} = \frac{1}{2} \times \frac{7}{2} \times \frac{7}{4}$$​​

Area=$$\frac{1}{2} \times \frac{49}{8}= \frac{49}{16}$$

Option (D) is right.