Question 84792: I don't know if this is the correct section for this. Find the distance between (-4,0) and (-5,-3). Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! This is a Pythagorean theorem problem.
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Notice that the distance between the x values of the two points that are given is a magnitude
of 1 which you can get by this subtraction: [-4 - (-5) = -4 + 5 = +1].
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The change in the y values will be at right angles to the change in the x values which
we found to be 1. The magnitude of the change in the y values is 3 which you can get by
the subtraction [0 - (-3) = 0 + 3 = 3].
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In summary the change in x is 1 and the change in y is 3. These are the legs of a right triangle
whose hypotenuse is the straight line distance between the points. Call this hypotenuse D
and you can then write the Pythagorean equation:
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The terms on the left side of this equation square out and you get:
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Add the two terms on the left side and you get:
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To find D just take the square root of both sides:
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And that's the answer you were looking for.
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It might help you to see what's going on in this method if you plot the two points and
then trace the horizontal path from the first point until you are directly over the second
point. At this this point trace the path vertically down to the second point. Then draw
a line connecting the two points. You should recognize the right triangle and be able to
see that the lengths of the two legs are 1 and 3 units long. The rest is just application
of the Pythagorean theorem which says that if you square the two legs and add these squares,
the result will equal the square of the hypotenuse which in this case is the direct line
distance between the two points. [Harder to explain this than it actually is. Once you
see what's going on, it becomes easier to work distance problems of this type.]
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Hope this helps you to see your way through distance problems when you are given two points.
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