What's the distance between (-3,5) & (8,1)

Question

What's the distance between the two points 

Answer 1

Hi, Lydia.  This question can be answered by the application of a formula called the "Distance Formula", which is as follows:  D=sqrt((X₂-X₁)²+(Y₂-Y₁)²).  In this formula D is the distance between the two coordinate points of interest, sqrt is the operation of taking the square-root of what is inside the outer parentheses, and the x's and y's are given by the coordinate points themselves.  While it is good practice to be organized in taking care of which set of coordinate points will be denoted with the subscript "2" or "1", fortunately, it will not matter for this particular calculation.  For example, (-3-8)²=(8-(-3))².

 

While this should be enough information to answer this question, to understand this formula conceptually, we can draw on a little Geometry.  If you were to draw a straight horizontal line from x=-3 to x=8 and a straight vertical line from y=5 to y=1 so that your two lines meet at a right angle, a third line drawn from your specified coordinate points would be the hypotenuse of a right triangle.  Because the hypotenuse's length has a specific relationship to the length of the legs of a right triangle, we use this to calculate the distance between the points.  The relationship is called "Pythagorean Theorem"  which states that a²+b²=c² where a and b are the lengths of the two legs (which can be calculated as the positive values of a=X₂-X₁ and b=Y₂-Y₁) and c is the length of the hypotenuse.  Solving for c by taking the square root of both sides gives us the Distance Formula!