Question

The area of the triangle formed by the line x/a+y/b=1 with the coordinate axes is

Answer 1

Here,
Line ; x/a + y/b = 1

for forming triangle we have require three non - colinear vertices.

this line cut in X - axis ,
when, y = 0
x/a + 0/b = 1

x = a hence, at X-axis it cuts (a , 0)

similarly cuts in Y-axis
when, x = 0

0/a + y/b = 1

y = b hence, at (0, b) it cuts in Y-axis.

now, we have three points (0, 0), (a , 0) and ( 0, b)

use co-ordinate Geometry formula for finding area of ∆ if points are given.

ar∆ = 1/2 { 0 + a( b - 0) + 0 }
= 1/2 ab


hence, area of ∆ = (ab)/2

Or in other method,

This is the intercept form of a line
x intercept is a
y intercept is b
after drawing this line on graph paper,we sees a right triangle

base of triangle is a
height of triangle is b
area of triangle =1/2 base*height
Area=ab/2