Question

if the points A (1,-9) B (a,-b) C (3,2) are collinear such that a-b=18 , then find a and b​

Answer 1

Answer:

let a =1

then 1-b=18

b=-17

now since let b =1

then a=18+1=19

Answer 2

Step-by-step explanation:

we know that if three points A,B and C are collinear, then AB+BC=AC

That is

$\sqrt{ {(a - 1)}^{2} + {( - b + 9)}^{2} } + \sqrt{ {(3 - a)}^{2} + {(2 + b)}^{2} } = \sqrt{ {(3 - 1)}^{2} + {(2 + 9)}^{2} }$

we also know that

$a - b = 18 \\ a = b + 18$

using this we can write

$\sqrt{ {(b+18 - 1)}^{2} + {( - b + 9)}^{2} } + \sqrt{ {(3 - b-18)}^{2} + {(2 + b)}^{2} } = \sqrt{ {(3 - 1)}^{2} + {(2 + 9)}^{2} }$

$\sqrt{ {(b+17)}^{2} + {( - b + 9)}^{2} } + \sqrt{ {( - b-15)}^{2} + {(2 + b)}^{2} } = \sqrt{ {(3 - 1)}^{2} + {(2 + 9)}^{2} }$