SOLUTION: find the distance between the pair of points (-1, -4) abd (-5, -7)

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Question 55427: find the distance between the pair of points (-1, -4) abd (-5, -7)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the point slope formula to find the horizontal and vertical distances between the points
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29m=slope
m=%28-7-%28-4%29%29%2F%28-5-%28-1%29%29Plug in x and y values of the points
m=%283%29%2F%284%29Simplify
Since the slope is 3/4, it really means between the points (-1, -4) and (-5, -7) the vertical distance ("rise") is 3 and the horizontal distance ("run") is 4. However, we want the diagonal distance between the points, which happens to be the hypotenuse of the vertical and horizontal lengths. So to find the hypotenuse we use Pythagoreans theorem to find it
a%5E2%2Bb%5E2=c%5E2Pythagoreans theorem: in this case a and b are known lengths and c is the hypotenuse
3%5E2%2B4%5E2=c%5E2Plug in known points
9%2B16=c%5E2Simplify
25=c%5E2
sqrt%2825%29=sqrt%28c%5E2%29isolate c by taking square root of both sides
c=5
So distance between the two points is 5 units