Question

Find the distance between the points given. (2, 2) and (5,5) 3 O 32 o 72

Answer 1

Answer:

$d = 3\sqrt{2}$

Explanation:

The distance between two distinct points on the same plane ($d$) can be calculated by the General Equation of the Line Segment, a derivation from the Pythagorean Theorem:

$d = \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}$ (1)

Where:

$(x_{A}, y_{A})$ - Initial point.

$(x_{B}, y_{B})$ - Final point.

If we know that $(x_{A}, y_{A}) = (2, 2)$ and $(x_B, y_B) = (5, 5)$, then the distance of the line segment is:

$d =\sqrt{(5-2)^{2}+(5-2)^{2}}$

$d = \sqrt{18}$

$d = 3\sqrt{2}$