SOLUTION: using pythsgorean theorem to find the distance, to the nearest tenth between points P(-10,1) and Q(5,5)?

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Question 214502: using pythsgorean theorem to find the distance, to the nearest tenth between points P(-10,1) and Q(5,5)?
Found 2 solutions by rfer, drj:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
c^2=a^2+b^2
c^2=4^2+15^2
c^2=16+225
c^2=241
c=15.5

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2=a%5E2%2Bb%5E2

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%5E2=d%5E2=%28x2-x1%29%5E2%2B%28y2-y1%29%5E2

d=sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29

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

d=sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29

d=sqrt%28%285-%28-10%29%29%5E2%2B%285-1%29%5E2%29

d=sqrt%2815%5E2%2B4%5E2%29

d=sqrt%28225%2B16%29

d=sqrt%28241%29=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