Answer:
The distance from N to T is : [tex]\sqrt{29}[/tex] or (square root of 29)
Step-by-step explanation:
From the given the diagram
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\mathrm{The\:distance\:between\:}\left(-2,\:-1\right)\mathrm{\:and\:}\left(3,\:1\right)\mathrm{\:is\:}[/tex]
[tex]=\sqrt{\left(3-\left(-2\right)\right)^2+\left(1-\left(-1\right)\right)^2}[/tex]
[tex]=\sqrt{\left(3+2\right)^2+\left(1+1\right)^2}[/tex]
[tex]=\sqrt{5^2+\left(1+1\right)^2}[/tex]
[tex]=\sqrt{5^2+2^2}[/tex]
[tex]=\sqrt{25+4}[/tex]
[tex]=\sqrt{29}[/tex]
Therefore, the distance from N to T is : [tex]\sqrt{29}[/tex] or (square root of 29)
