Question

Find the distance between the two points (2,5) and (6,-1)

Answer 1

`\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 = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√((6-2)^2+(-1-5)^2)\implies d=√(4^2+(-6)^2) \\\\\\ d=√(16+36)\implies d=√(52)\implies d=2√(13)`

Answer 2

=
`√(52)` units

Explanation:

x₁ = 2 ; y₁ = 5

x₂ = 6 ; y₂ = -1

D =
`√((x₂ - x₁)² + (y₂ - y₁)²)`

=
`√((6 - 2)² + (-1 -5)²)`

=
`√(4² + (-6)²)`

=
`√(16 + 36)`

D =
`√(52)` units