The distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . (x_1,y_1)\text{ and }(x_2,y_2)\text{ is }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}. ( x 1 , y 1 ) and ( x 2 , y 2 ) is ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . Using this distance formula we obtain:
1.a. The distance between (3,4) and (5,2) is ( 5 − 3 ) 2 + ( 2 − 4 ) 2 = 4 + 4 = 8 = 2 2 . \sqrt{(5-3)^2+(2-4)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}. ( 5 − 3 ) 2 + ( 2 − 4 ) 2 = 4 + 4 = 8 = 2 2 .
b. The distance between (0,6) and (4,0) is 4 2 + 6 2 = 16 + 36 = 52 = 2 13 . \sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}. 4 2 + 6 2 = 16 + 36 = 52 = 2 13 .
2. The distance between the points ( b , 3 ) and ( − b , 2 ) is ( − b − b ) 2 + ( 2 − 3 ) 2 = 4 b 2 + 1 . (b,3)\text{ and }(-b,2)\text{ is } \sqrt{(-b-b)^2+(2-3)^2}=\sqrt{4b^2+1}. ( b , 3 ) and ( − b , 2 ) is ( − b − b ) 2 + ( 2 − 3 ) 2 = 4 b 2 + 1 .
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