Question

The area of the triangle formed by the line x by a + y by b = 1 with the co-ordinate axes is
(a) ab
(b) 2ab
(d) 1 by 2 ab
(c) 1 by 4 ab​

Answer 1

Answer:

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

Answer 2

Answer:

The line x/a + y/b = 1,

intercepts x and y axes at a and b

(0,0) ; (a, 0) ; (0,b) are the three vertices of triangle

therefore,

area of triangle = ½ab