Question

if the points (a,0), (0,b) and (3,2) are collinear, prove that 2/b+3/a=1

Answer 1

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Answer 2

Answer:

If the points (a,0), (0,b) and (3,2) are collinear, then $\frac{2}{b}+\frac{3}{a}=1$

Step-by-step explanation:

The given points are (a,0), (0,b) and (3,2).

If three points $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ are collinear, then

$\frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}$

$\frac{b-0}{0-a}=\frac{2-b}{3-0}$

$\frac{b}{-a}=\frac{2-b}{3}$

$3b=-a(2-b)$

$3b=-2a+ab$

Divide both sides by ab.

$\frac{3b}{ab}=-\frac{2a}{ab}+\frac{ab}{ab}$

$\frac{3}{a}=-\frac{2}{b}+1$

$\frac{2}{b}+\frac{3}{a}=1$

Hence proved.