Question

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

• A. -63
• B. 63
• C. 60
• D. -60

Answer 1

The correct option is A

-63

It is given that the three points A(x, 2), B (-3,-4) and C (7, -5) are collinear.
$\therefore Areaof\Delta ABC=0$
$\Rightarrow \frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]=0$
Here, $x_1=x,y_1=2,x_2=-3,y_2=-4and{x}_3=7,y_3=-5$
$\Rightarrow x[-4-(-5\left)\right]-3(-5-2)+7[2-(-4\left)\right]=0\Rightarrow x(-4+5)-3(-5-2)+7(2+4)=0\Rightarrow x-3\times (-7)+7\times 6=0\Rightarrow x+21+42=0\Rightarrow x+63=0\Rightarrow x=-63$
Thus, the value of x is -63.
Hence, the correct option is A.