The area of the triangle formed by the line xa+yb=1 with the coordinate axes is:

We have been given the lines

x = 0

y = 0

and

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

.
We need to find the area of the triangle formed by the line

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

with the coordinate axes.
Substitute 0 for y in

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

to find the x intercept of the line.

\frac{x}{a} + \frac{0}{b} = 1

\Rightarrow \frac{x}{a} + 0 = 1

\Rightarrow \frac{x}{a} = 1

\Rightarrow x = a

Substitute 0 for x in

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

to find the y intercept of the line.

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

\Rightarrow \frac{0}{a} + \frac{y}{b} = 1

\Rightarrow 0 + \frac{y}{b} = 1

\Rightarrow \frac{y}{b} = 1

\Rightarrow y = b

Thus, we have three coordinates, (0,0), (a, 0), (0, b).
On plotting the points on a graph, we get,

Now, the area of the triangle formed by the line

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

with the coordinate axes is equal to the area of triangle ABC.
The formula of the area of a triangle is,

A = \frac{1}{2} \times base \times height

\Rightarrow A = \frac{1}{2} \times AB \times AC

\Rightarrow A = \frac{1}{2} \times a \times b

Hence, the area of triangle is

A = \frac{1}{2} ab

.
Hence, option 3 is correct.

The area of the triangle formed by the line $\frac{x}{a} + \frac{y}{b} = 1$ with the coordinate axes is: