If the points A(1, 2),O(0, 0),and C(a, b) are | vedclass

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(C) Let the given points be $A(x_1, y_1) = (1, 2)$,$O(x_2, y_2) = (0, 0)$,and $C(x_3, y_3) = (a, b)$.Since the points are collinear,the area of the tr

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$2a = b$

Vedclass · Answer

(C) Let the given points be $A(x_1, y_1) = (1, 2)$,$O(x_2, y_2) = (0, 0)$,and $C(x_3, y_3) = (a, b)$.Since the points are collinear,the area of the triangle formed by these points must be zero.The formula for the area of a triangle is $\Delta = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$.Substituting the given coordinates:$0 = \frac{1}{2} |1(0 - b) + 0(b - 2) + a(2 - 0)|$.$0 = \frac{1}{2} |-b + 0 + 2a|$.$0 = \frac{1}{2} |2a - b|$.This implies $2a - b = 0$,or $2a = b$.Hence,the required relation is $2a = b$.

If the points $A(1, 2)$,$O(0, 0)$,and $C(a, b)$ are collinear,then:

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