Question

Find the length of the segment. round to the nearest tenth of a unit P(1,2) Q(5,4)

Answer 1

Hello, 

$d= \sqrt{ (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} } \\ \\ d=\sqrt{ (5-1)^{2}+(4-2)^{2} } \\ \\ d=\sqrt{ 4^{2}+2^{2} } \\ \\ d= \sqrt{16+4} \\ \\ d= \sqrt{20} \\ \\d= \sqrt{2^{2}*5 }\\ \\d= 2\sqrt{5 } \\ \\ d=4.5$

Answer: lenght= 4.5

Answer 2

$P(1,2)\ \ \ Q(5,4)\\\\ PQ=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}\\\\ PQ=\sqrt{(5-1)^2+(4-2)^2}=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}\approx4,5\\\\ Length\ of\ this\ segment\ is\ equal\ to\ 4,5.$