Question

For what value of a the point (a, 1), (1, –1) and (11, 4) are collinear?

Answer 1

Let A(a, 1), B(1, –1) and (11, 4) be the given point 

Area of ΔABC 

`=1/2{a(-1-4)+1(4-1)+11(1+1)} ` 

`=1/2 {-5+3+22}` 

`=1/2{-5a+25}` 

For the point to be collinear 

Area of ΔABC = 20  

`1/2{-5a+25}=0` 

`=>-5a+25=0`

`=>-5a=-25` 

`=>a=5`