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The Mid-Point Theorem

Find the rati...

Question

Find the ratio of x coordinate to y coordinate of incentre of a triangle whose midpoint of its sides are $(0, 1), (1, 1), (1, 0)$

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Solution

$∴$ Coordinates of $A (2, 0)$
Coordinates of $B (0, 2)$
Coordinates of $C (0, O)$
$A B = c = 2 \sqrt{2} A C = b = 2 \sqrt{2} B C = a = 2 \sqrt{2} A s t h e s i d e s a r e e q u a l s o e q u i l a t e r a l t r i a n g l e ∴ I n c e n t r e i s (\frac{2 + 0 + 0}{3}, \frac{0 + 2 + 0}{3}) = (\frac{2}{3}, \frac{2}{3}) ∴ R a t i o = 1$

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