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Distance between Two Points on the Same Coordinate Axes

Column II giv...

Question

Column II gives distance between pair of points given in column I match them correctly.

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Solution

$A) L e t t h e c o - o r d i n a t e s o f A & B a r e A (x_{1}, y_{1}) = (- 5, 7) & B (x_{2}, y_{2}) = (- 1, 3) r e s p e c t i v e l y . T h e n A B = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(- 5 + 1)}^{2} + {(7 - 3)}^{2}} u n i t s = 4 \sqrt{2} u n i t s . ⟹ M a t c h e s w i t h 4. B) L e t t h e c o - o r d i n a t e s o f A & B a r e A (x_{1}, y_{1}) = (5, 4) & B (x_{2}, y_{2}) = (1, 3) r e s p e c t i v e l y . T h e n A B = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(1 - 5)}^{2} + {(4 - 3)}^{2}} u n i t s = \sqrt{17} u n i t s . ⟹ M a t c h e s w i t h 1. C) L e t t h e c o - o r d i n a t e s o f A & B a r e A (x_{1}, y_{1}) = (\sqrt{3} + 1, 1) & B (x_{2}, y_{2}) = (0, \sqrt{3}) r e s p e c t i v e l y . T h e n A B = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(\sqrt{3} + 1 - 0)}^{2} + {(1 - \sqrt{3})}^{2}} u n i t s = \sqrt{8} u n i t s . ⟹ M a t c h e s w i t h 2. D) L e t t h e c o - o r d i n a t e s o f A & B a r e A (x_{1}, y_{1}) = (0, 0) & B (x_{2}, y_{2}) = (- \sqrt{3}, \sqrt{3}) r e s p e c t i v e l y . T h e n A B = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(\sqrt{3} - 0)}^{2} + {(- \sqrt{3 - 0})}^{2}} u n i t s = \sqrt{6} u n i t s . ⟹ M a t c h e s w i t h 3. A n s - A ⟶ 4 B ⟶ 1 C ⟶ 2 D ⟶ 3$

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