MTH 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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???Find the value of k so that the given points are sqrt(29) units apart???
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I dont know how to set this problem up. I know we are using the distance formula. I just cant figure out how to set it up to find the points we are looking for.
You didn't include all the details of the given problem, but I think I know how this particular problem is set up. Here's a variation on it:
Find a value of k such that the points (4, 7) and (9, k) are sqrt(29) units apart.
To solve this, write the expression for the distance between the points, which is
dist between points = sqrt( (9 - 4)^2 + (k - 7)^2).
You know this distance is sqrt(29), so write what you now know as an equation:
sqrt( (9 - 4)^2 + (k - 7)^2) = sqrt(29).
It's fairly straightforward to solve this equation:
square both sides to get
(9 - 4)^2 + (k - 7)^2 = 29
5^2 + (k^2 - 14 k + 49) = 29
k^2 - 14 k + 74 = 29
k^2 - 14 k + 45 = 0
This is a quadratic equation which is easily solved either using the quadratic formula, or in this case by factoring. Our solutions are k = 9 and k = 5.
Thus the second point (9, k) becomes either (9, 5) or (9, 9). You can verify that each of these points lies at distance sqrt(29) from (4, 7).