What is the distance between the points (2, 1) and (14, 6) on a coordinate plane?

Question

I dont get the distance, im just looking for the answer

Answer 1

In the Cartesian Coordinate System, points are described using the notation (x,y) for their coordinates.

 

Since the x-axis and the y-axis are at right angles to each other, the distance between two points, for example, (x₁,y₁) and (x₂,y₂) is the hypotenuse of the right triangle that the points form.  So, the distance between them is:

    D = √((y₂-y₁)² + (x₂-x₁)²))

 

This is known as "the Distance Formula."

 

The distance between the points (2,1) and (14,6) is:

    D = √((6-1)² + (14-2)²))

    D = √( 25 + 144 )

    D = √169

    D = 13

 

Now, you should start to notice problems like this that have "nice, neat" results (for example, a whole number).  That's because the person who developed the problem wanted to make to calculations easy so you could concentrate for solving the problem.  The numbers (5,12,13) are one of many sets called "Pythagorean Triples" that you may see in many, many problems.  How about these (see Wikipedia):

  (3, 4, 5)        (5, 12, 13)     (8, 15, 17)
(7, 24, 25)     (20, 21, 29)    (12, 35, 37)
(9, 40, 41)     (28, 45, 53)    (11, 60, 61)
(16, 63, 65)   (33, 56, 65)    (48, 55, 73)
(13, 84, 85)   (36, 77, 85)    (39, 80, 89)
(65, 72, 97)   

Answer 2

d = sqrt[(14-2)^2 + (6-1)^2] = sqrt(144 + 25) = 13