Question

Find the distance between the points (-3,2) and (0,3).

Answer 1

Answer:

The distance between (-3, 2) and (0,3) is √10.

Step-by-step explanation:

As we go from (-3,2)  to  (0,3), x increases by 3 and y increases by 1.

Think of a triangle with base 3 and height 1.  Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):

distance = √(3² + 1²) = √10

The distance between (-3, 2) and (0,3) is √10.

Answer 2

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:

$(x_ {1}, y_ {1}): (- 3,2)\\(x_ {2}, y_ {2}) :( 0,3)$

Substituting:

$d = \sqrt {(0 - (- 3)) ^ 2+ (3-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (1) ^ 2}\\d = \sqrt {9 + 1}\\d = \sqrt {10}$

Answer:

The distance between the points is $\sqrt {10}$