Question

If (1,1) devides the line segment AB in the ratio 1:2 when A(a+b,a-b) and B(a-b,a+b) then find the values of ‘a’ and ‘b’

Answer 1

We find a = 1, b = 0

Step-by-step explanation:

The given points are A (a+b, a-b) and B (a-b, a+b).

Then the coordinates of the point which divides the line segment AB in the ratio 1 : 2 are

( 2(a + b) + 1(a - b)/(1 + 2), 2(a - b) + 1(a + b)/(1 + 2) )

i.e., ( (2a + 2b + a - b)/3, (2a - 2b + a + b)/3 )

i.e., ( (3a + b)/3, (3a - b)/3 )

By the given condition,

(3a + b)/3 = 1 or, 3a + b = 3 ..... (1)

(3a - b)/3 = 1 or, 3a - b = 3 ..... (2)

Adding (1) and (2), we get

3a + b + 3a - b = 3 + 3

or, 6a = 6

or, a = 1

Then b = 3 - 3 (1) = 3 - 3 = 0

i.e., b = 0

Therefore the value of a is 1 and of b is 0.

Answer 2

Step-by-step explanation:

this may help you

the value of a=1 and b=2