Answer:
= [tex]\sqrt{52}[/tex] units
Step-by-step explanation:
x₁ = 2 ; y₁ = 5
x₂ = 6 ; y₂ = -1
D = [tex]\sqrt{(x₂ - x₁)² + (y₂ - y₁)²}[/tex]
=[tex]\sqrt{(6 - 2)² + (-1 -5)²}[/tex]
=[tex]\sqrt{4² + (-6)²}[/tex]
= [tex]\sqrt{16 + 36}[/tex]
D = [tex]\sqrt{52}[/tex] units
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(6-2)^2+(-1-5)^2}\implies d=\sqrt{4^2+(-6)^2} \\\\\\ d=\sqrt{16+36}\implies d=\sqrt{52}\implies d=2\sqrt{13}[/tex]
