Answer:
[tex]d = 3\sqrt{2}[/tex]
Explanation:
The distance between two distinct points on the same plane ([tex]d[/tex]) can be calculated by the General Equation of the Line Segment, a derivation from the Pythagorean Theorem:
[tex]d = \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex] (1)
Where:
[tex](x_{A}, y_{A})[/tex] - Initial point.
[tex](x_{B}, y_{B})[/tex] - Final point.
If we know that [tex](x_{A}, y_{A}) = (2, 2)[/tex] and [tex](x_B, y_B) = (5, 5)[/tex], then the distance of the line segment is:
[tex]d =\sqrt{(5-2)^{2}+(5-2)^{2}}[/tex]
[tex]d = \sqrt{18}[/tex]
[tex]d = 3\sqrt{2}[/tex]
