The point C divides the line segment in the ratio 4:9. Find the length of AC if the line segment AB is 26 cm long

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Solution

Given, point C divides the line segment in the ratio 4:9
$∴ \frac{A C}{B C}$ = $\frac{4}{9}$

Therefore, $\frac{A B}{A C}$ = $\frac{A C}{A C}$ + $\frac{B C}{A C}$ = 1+ $\frac{9}{4}$ = $\frac{13}{4}$

$\frac{A C}{A B}$ = $\frac{4}{13}$ . So,AC=AB $\times$ $\frac{4}{13}$ = $\frac{4}{13} \times 26$ = 8 cm

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