Question

The area of the triangle formed by the line x/a + y/b =1 with the coordinate axes is
A. ab
B. 2ab
C. ½ ab D. ¼ ab

Answer 1

Answer:1 /2 ab

Solution:

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 axis at a and b

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

therefore,

area of triangle = ½ab