Answer:
[tex]\mathrm{Distance\:between\:}\left(-2,\:3\right)\mathrm{\:and\:}\left(2,\:4\right)=\sqrt{17}[/tex]
Step-by-step explanation:
Given the points
Finding the distance between the points (-2, 3) and (2, 4) is
[tex]\mathrm{The\:distance\:between\:}\left(-2,\:3\right)\mathrm{\:and\:}\left(2,\:4\right)\mathrm{\:is\:}[/tex]
[tex]=\sqrt{\left(2-\left(-2\right)\right)^2+\left(4-3\right)^2}[/tex]
[tex]=\sqrt{\left(2+2\right)^2+\left(4-3\right)^2}[/tex]
[tex]=\sqrt{4^2+1}[/tex]
[tex]=\sqrt{16+1}[/tex]
[tex]=\sqrt{17}[/tex]
Therefore, the distance between the points (-2, 3) and (2, 4):
[tex]\mathrm{Distance\:between\:}\left(-2,\:3\right)\mathrm{\:and\:}\left(2,\:4\right)=\sqrt{17}[/tex]
