amorphous wrote:
In the xy-coordinate system, the distance between points \((2\sqrt{3}, - \sqrt{2})\) and \((5\sqrt{3}, 3\sqrt{2})\) is approximately
A 4.1
B 5.9
C 6.4
D 7.7
E 8.1
The distance between two points in xy co-ordinates : \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)
So here the distance between two points = \(\sqrt {(5\sqrt{3} - 2\sqrt{3})^2 + (3\sqrt{2} + \sqrt{3})^2} = \sqrt {(3\sqrt{3})^2 + (4\sqrt{2})^2} = \sqrt {27 + 32} = \sqrt{59} = 7.7\)
*** Please note
\(\sqrt{59}\)= nearly equals to 7.7
since \(\sqrt{64} = 8\)and \(\sqrt{49} = 7\)
so \(\sqrt{59}\)should be between 7 and 8, so only option D satisfy