State whether the following statements are true or false.
Enter 1 for true and 0 for false
The point A (2, 7) lies on the perpendicular bisector of line segment joining
the points P (6, 5) and Q (0, 4).

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Solution

$T h e p o i n t A (x_{1}, y_{1}) = (2, 7) w i l l l i e o n t h e ⊥ b i s e c t o r o f a l i n e P Q j o i n i n g P (x_{2}, y_{2}) = (6, 5) & Q (x_{3}, y_{3}) = (0, 4) i f A P = A Q . A p p l y i n g t h e d i s t a n c e f o r m u l a d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} w e g e t A P = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} = \sqrt{{(6 - 2)}^{2} + {(5 - 7)}^{2}} = \sqrt{20} a n d A Q = \sqrt{{(x_{3} - x_{1})}^{2} + {(y_{3} - y_{1})}^{2}} = \sqrt{{(0 - 2)}^{2} + {(4 - 7)}^{2}} = \sqrt{13} . ∴ A P \neq A Q . i . e A d o e s n o t l i e o n t h e ⊥ b i s e c t o r o f t h e l i n e P Q . S o t h e g i v e n s t a t e m e n t i s n o t v a l i d . A n s - F A L S E .$

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