Question

using distance formula show that give pts are collinear (1,-1),(5,2) and (9,5)

Answer 1

As we're supposed to use distance formula, we do the following steps.
1)Take 3 points A,B,C
2) Calculate AB, BC, and AC
3)If AB+BC=AC, or AB-BC= AC( coz the order May differ), then they're proven to be collinear.

Hope this helps, else comment, I'll try to send calculations.

Answer 2

let a(1,-1);b(5,2);c(9,5)
ab distance√(5-1)2+(2+1)2=√16+9=√25=5
bc distance=√(9-5)2+(5-2)2=√(4)2+(3)2=5
ca distance=√(9-1)2+(5+1)2=√(8)2+(6)2=√64+36=10
we know the sum of any two sides equal to third side then it is said to be collinear
therfore
ab+bc=ca