If the points A(x, 2), B(−3, −4) and C(7, −5) are collinear then the value of x is

Let A(x1 = x, y1 = 2), B(x2 = −3, y2 = −4) and C(x3 = 7, y3 = −5) be collinear points. Then

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

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

$\Rightarrow x+21+42=0$

$\Rightarrow x=-63$

Hence, the correct answer is option (a).