What is the condition for the points (a, 0),( | vedclass

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(B) For three points $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ to be collinear,the area of the triangle formed by them must be zero.Alternatively,the

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$\frac{1}{a} + \frac{1}{b} = 1$

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(B) For three points $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ to be collinear,the area of the triangle formed by them must be zero.Alternatively,the slope between any two pairs of points must be equal.Let the points be $A(a, 0)$,$B(0, b)$,and $C(1, 1)$.Slope of $AB = \frac{b - 0}{0 - a} = -\frac{b}{a}$.Slope of $BC = \frac{1 - b}{1 - 0} = 1 - b$.Equating the slopes: $-\frac{b}{a} = 1 - b$.$-b = a(1 - b) \implies -b = a - ab$.Rearranging the terms: $ab = a + b$.Dividing both sides by $ab$ (assuming $a, b 
eq 0$): $1 = \frac{a}{ab} + \frac{b}{ab}$.Therefore,$1 = \frac{1}{b} + \frac{1}{a}$ or $\frac{1}{a} + \frac{1}{b} = 1$.

What is the condition for the points $(a, 0)$,$(0, b)$,and $(1, 1)$ to be collinear?

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