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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

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#### Solution

It is given that the three points A(*x*, 2), B(−3, −4) and C(7, −5) are collinear.

∴ Area of ∆ABC = 0

`=1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=0`

Here `x_1=x, y_1=2, x_2=-3, y_2=-4, x_3=7 and y_3=-5`

⇒x[−4−(−5)]−3(−5−2)+7[2−(−4)]=0

⇒x(−4+5)−3(−5−2)+7(2+4)=0

⇒x−3×(−7)+7×6=0

⇒x+21+42=0

⇒x+63=0

⇒x=−63

Thus, the value of x is − 63.

Hence, the correct option is A

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