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Distance Formula

The abscissa ...

Question

The abscissa of a point A is twice its ordinate and $B \equiv (10, 0) .$ Find the co-ordinates of A if $A B = 5$ units.

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Solution

$g i v e n x = 2 y, w h e r e (x, y) i s c o - o r d i n a t e o f A A B = 5 \sqrt{(x - 10)^{2} + (y - 0)^{2}} = 5 (2 y - 10)^{2} + y^{2} = 5^{2} 4 y^{2} - 40 y + 100 + y^{2} = 25 5 y^{2} - 40 y + 75 = 0 y^{2} - 8 y + 15 = 0 y^{2} - 5 y - 3 y + 15 = 0 y (y - 5) - 3 (y - 5) = 0 (y - 3) (y - 5) = 0 ∴ y = 3 o r y = 5 I f y = 3 t h e n x = 6 ∴ p o i n t (6, 3) I f y = 5 t h e n x = 10 ∴ p o i n t (10, 5)$

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