SOLUTION: I think this is the correct place to put this. I'm doing a practice packet I have to turn in on the first day of school. Here are the problems.
Find the distance between the giv
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Find the distance between the giv
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Question 92035: I think this is the correct place to put this. I'm doing a practice packet I have to turn in on the first day of school. Here are the problems.
Find the distance between the given points.
1. (-5,-7) and (7, 9)
2. (6, -17) and (18, -5)
If you could tell me the formula and what to do I think I can get it. (Step by step please) Found 2 solutions by stanbon, bucky:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! You might recognize this as a Pythagorean theorem problem. If you think about it a little
you can see that the change in the x distances (horizontal) between the two points is one leg of a
right triangle, and the change in the y distances (vertical) between the two points is the
other leg. Then the hypotenuse of the right triangle is the distance between the two points.
.
Plot the two points on a graph. Then extend a vertical line through each point and a horizontal
line through each point. Where the vertical line intersects with the horizontal line is
the vertex of a right angle. Now draw a line that connects the two points. Notice how
it is the hypotenuse of a right triangle formed by the horizontal line, the vertical, line
and the line connecting the two points. Let's try one of your problems to give you the
idea. Take the points (-5,-7) and (7,9)
.
Notice that the change in x is from -5 to +7, a distance of 12. Then notice that the change
in y is from -7 to +9, a distance of 16.
.
Now recall from geometry that the Pythagorean theorem says that the sum of the squares
of the two legs of a right triangle is equal to the square of the hypotenuse. If one leg is x
and the other leg is y and the hypotenuse (longest side) is h, then the equation form of the
Pythagorean theorem can be written as:
.
.
For this problem we found that x = 12 and y = 16. Substituting these values gives:
.
.
And squaring each of the numbers on the left side results in:
.
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Adding the two numbers on the left side:
.
.
and solve for the distance h by taking the square root of both sides to get:
.
.
Hope this explanation helps you to understand why the distance equation works the way it does.
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