Question

What is the distance in the standard (x, y) coordinate plane between the points (2,3) and (5,5)?

Answer 1

The distance between the points (2,3) and (5,5) is 3.6 units

Solution:

Distance between two points is given by:

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

We have to find the distance in the standard (x, y) coordinate  plane between the points (2,3) and (5,5)

From given,

$(x_1, y_1) = (2, 3)\\\\(x_2, y_2) = (5, 5)$

Substituting the values we get,

$d = \sqrt{(5-2)^2 + (5-3)^2}\\\\Simplify\\\\d = \sqrt{3^2 + 2^2}\\\\d = \sqrt{9+4}\\\\d = \sqrt{13}\\\\In\ decimal\ form\\\\d = 3.605 \approx 3.6$

Thus distance between the points (2,3) and (5,5) is 3.6 units