Question

if points (a,o) ,(0,b) and( x,y) are collinear then prove that x/a+y/b=1

Answer 1

Here is your answer


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Answer 2

Answer:

$If \: given \: three \: points\\are \: collinear ,\: then \: \frac{x}{a}+\frac{y}{b}=1$

Step-by-step explanation:

Let A(a,0),B(0,b) and C(x,y) are collinear .

Slope of AB = Slope of BC

$\frac{b-0}{0-a}=\frac{y-b}{x-0}$

$\implies \frac{b}{-a}=\frac{y-b}{x}$

$\implies bx=(-a)(y-b)$

$\implies bx=-ay+ab$

$\implies bx+ay=ab$

/* Divide each term by ab ,we get

$\implies \frac{bx}{ab}+\frac{ay}{ab}=\frac{ab}{ab}$

$\implies \frac{x}{a}+\frac{y}{b}=1$

Therefore,

$If \: given \: three \: points\\are \: collinear ,\: then \: \frac{x}{a}+\frac{y}{b}=1$

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