# If (x , 2), (−3, −4) and (7, −5) are collinear, then x =

Question:

If (x , 2), (−3, −4) and (7, −5) are collinear, then x =

(a) 60

(b) 63

(c) −63

(d) −60

Solution:

We have three collinear points $\mathrm{A}(x, 2) ; \mathrm{B}(-3,-4) ; \mathrm{C}(7,-5)$.

In general if $\mathrm{A}\left(x_{1}, y_{1}\right) ; \mathrm{B}\left(x_{2}, y_{2}\right) ; \mathrm{C}\left(x_{3}, y_{3}\right)$ are collinear then,

$x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)=0$

So,

$x(-4+5)-3(-5-2)+7(2+4)=0$

So,

$x+42+21=0$

Therefore,

$x=-63$