Question

The mid point of the line segment joining (4a, 2b – 3) and (−4, 3b) is (2, –2a). Find the values of a and b.

Answer 1

It is given that the mid-point of the line segment joining (4a, 2b – 3) and (−4, 3b) is (2, –2a).

∴ `(2, -2a) = ((4a - 4)/2,(2b - 3 + 3b)/2)`

`=> 2 = ((4a - 4)/2)`

`=>` 4a − 4 = 4

`=>` 4a = 8

`=>` a = 2

Also,

`-2a = (2b - 3 + 3b)/2`

`=> -2 xx 2 = (5b - 3)/2`

`=>` 5b − 3 = −8

`=>` 5b = −5

`=>` b = −1