The distance between the two points is [tex]2\sqrt{10}[/tex]
Step-by-step explanation:
The given coordinates is [tex](-2,1)[/tex] and [tex](4,3)[/tex]
To find the distance between two points, let us use the distance formula,
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex] where [tex]\left(x_{1}, y_{1}\right)=(-2,1)[/tex] and [tex]\left(x_{2}, y_{2}\right)=(4,3)[/tex]
Thus, substituting the values in the formula, we get,
[tex]d=\sqrt{(4+2)^{2}+(3-1)^{2}}[/tex]
Simplifying the expression,
[tex]\begin{aligned}d &=\sqrt{(6)^{2}+(2)^{2}} \\&=\sqrt{36+4} \\&=\sqrt{40} \\&=2 \sqrt{10}\end{aligned}[/tex]
Thus, the distance between the two points is [tex]2\sqrt{10}[/tex]
