If three points `(x_1,y_1),(x_2, y_2),(x_3, y_3)` lie on the same line, prove that `(y_1-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0`

Explanation

Given,
Points `(x_1,y_1),(x_2,y_2),(x_3,y_3)` lie on same line so they are collinear


thus,

`(x_1y_2+x_2y_3+x_3y_1)−(x_2y_1+x_3y_2+x_1y_1)=0`


`=>(x_1y_2−x_1y_3)+(x_2y_3−x_2y_1)+(x_3y_1−x_3y_2)=0
`

`=>x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2)=0`
...