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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
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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