Question

Find the distance between the points (31) and (10, 5).
Write your answer as a whole number or a simple radical expression. Do not round
units

Answer 1

For this case we have that by definition, the distance between two points is given by:

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

We have the following points:

$(x_ {1}, y_ {1}): (3,1)\\(x_ {2}, y_ {2}): (10,5)$

Substituting we have:

$d = \sqrt {(10-3) ^ 2 + (5-1) ^ 2}\\d = \sqrt {(7) ^ 2 + (4) ^ 2}\\d = \sqrt {49 + 16}\\d = \sqrt {65}$

Answer:

The distance between the points is $\sqrt {65}$