Question 214502
Using the Pythagorean Theorem to find the distance, to the nearest tenth between points P(-10,1) and Q(5,5)?


Step 1.  The Pythagorean Theorem says that the sum of the squares of the sides (a and b) is equal to the square of the hypotenuse (c).  This can be expressed as 


{{{c^2=a^2+b^2}}}


Step 2.  The sides are the differences of the x-coordinates and the differences of the the y-coordinates.  The hypotenuse is the distance d between the two points.


So let's find d in general where  P(x1,y1) and Q(x2,y2).  Then 


{{{a=x2-x1}}}


{{{b=y2-y1}}}


{{{c^2=d^2=(x2-x1)^2+(y2-y1)^2}}}


{{{d=sqrt((x2-x1)^2+(y2-y1)^2)}}}


Step 3.  So for P(-10,1) and Q(5,5) then x1=-10, y1=1, x2=5, and y2=5


{{{d=sqrt((x2-x1)^2+(y2-y1)^2)}}}


{{{d=sqrt((5-(-10))^2+(5-1)^2)}}}


{{{d=sqrt(15^2+4^2)}}}


{{{d=sqrt(225+16)}}}


{{{d=sqrt(241)=15.524=15.5}}}


Step 4.  The distance between the given two points is d=15.5


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J