# What is a if points (1,3),(2,1),(a,a-4) coliniars ?

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### 1 Answer

A(1,3) ,B(2,1) and C(a,a-4)

If A,B and C are colinear then area of triangle formed by ABC s zero.

`arDelta ABC=(1/2)|[1,3,1],[2,1,1],[a,a-4,1]|=0`

`(1/2){1(1xx1-1xx(a-4))-3(2xx1-axx1)+1(2xx(a-4)-1xxa)}=0`

`(1/2){1(1-a+4)-3(2-a)+1(2a-8-a)}=0`

`5-a-6+3a+a-8=0`

`3a-9=0`

`3a=9`

`a=3`

Thus A(1,3),B(2,1) and C(3,-1) are colinear