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Introduction to Curves

State whether...

Question

State whether the following statements are true or false.
Enter $1$ for true and $0$ for false
The points (0, 5), (0, 9) and (3, 6) are collinear.

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Solution

$L e t t h e g i v e n p o i n t s b e A (0, 5), B (0, 9) & C (3, 6) . T h e a b s c i s s a e o f A & B a r e 0. ∴ A & B l i e o n t h e Y - a x i s . B u t t h e c o - o r d i n a t e s o f C a r e n o n z e r o p o s i t i v e n u m b e r s . ∴ C l i e s i n t h e I q u a r d r a n t . S o i t i s i m p o s s i b l e f o r A, B & C t o l i e o n t h e s a m e l i n e i . e t h e y a r e n o n - c o l l i n e a r p o i n t s . ∴ T h e g i v e n s t a t e m e n t i s f a l s e . A n s - F A L S E .$

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