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Question 87944: what is the distance between (-3,-2) and (1,4)
A) square root of 10
B) 27
C) 2 square root of 5
D) 18 square root of 3
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Something is wrong here.
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The distance between the two points is found by using the Pythagorean theorem. The change in
x values gives you one leg of the triangle, and the change in y values gives you the other
leg.
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Let's compute the change in x. In one of the points the x-value is -3. In the other point
the x-value is +1. So x goes from -3 to +1 and that is a distance of 4 units.
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Now let's compute the change in y. In one of the points the y-value is -2, and in the other
point it is +4. So y goes from -2 to +4 and that is a distance of 6 units.
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So we know that the two legs of the right triangle are 4 and 6. The hypotenuse of the
triangle is the distance between the points. The Pythagorean theorem tells us that the
sum of the squares of the two legs is the hypotenuse squared. In equation form this is:
.
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where a is one of the legs, b is the other leg, and c is the distance we are looking for.
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Let's call a the x distance of 4 and b the y distance of 6. Substituting these values we
get:
.
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and squaring out the terms on the left side results in:
.
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Adding the terms on the left side simplifies the equation to:
.
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Now solve for c by taking the square root of both sides to get:
.
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If you use a calculator to find  you get  .
So the distance between the two points you were given is 7.211102551 units.
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But none of your answers matches that value.
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Answer a) is square root of 10 and in your head you can tell that it has to be a little bigger
than square root of 9 which is 3 but it is less than the square root of 16 which is 4.
Therefore, answer a) is between 3 and 4, which means that it can't match our answer of
7.211102551.
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Answer b) is 27. That definitely doesn't match our answer.
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Answer c) is  and you know that  is less than 
which is 3. So must be less than  and that means that answer c) is
less than 6. Therefore, it doesn't match our answer.
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Finally, Answer d) is  . You know that  is greater than 1. If
it were just 1, then this answer would be  . So this answer is greater than
18. Therefore, it can't be our answer of 7.211102551.
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None of the answers matches.
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Like I said at the beginning ... something is wrong here with this problem.
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Hope this helps you to see your way through the problem. The answer you are trying to
match (assuming that the points are correct) is .
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