SOLUTION: I have a question that I cannot work out. It is: Find the possible values of y if the points (-7,-9) and (-10, y) are a distance d=squareroot 178 apart. Hod do I do this?

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Question 84774: I have a question that I cannot work out. It is: Find the possible values of y if the points (-7,-9) and (-10, y) are a distance d=squareroot 178 apart. Hod do I do this?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the possible values of y if the points (-7,-9) and (-10, y) are a distance d=squareroot 178 apart. Hod do I do this?
:
Remember the distance formula:
d = sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29; In this problem: x1 = -7, x2 = -10; y1 = -9; y2 = y
:
Substitute for x1, x2, y1, y2, and d
sqrt%28%28-10-%28-7%29%29%5E2+%2B+%28y-%28-9%29%29%5E2%29 = sqrt%28178%29
:
sqrt%28%28-10%2B7%29%5E2+%2B+%28y%2B9%29%29%5E2%29 = sqrt%28178%29
:
Squaring both sides gets rid of the radicals:
%28-10%2B7%29%5E2+%2B+%28y%2B9%29%5E2 = 178
:
-3%5E2+%2B+%28y%5E2+%2B+18y+%2B+81%29 = 178
:
y^2 + 18y + 81 + 9 - 178 = 0
:
y^2 + 18y - 88 = 0
:
Factors to:
(y + 22)(y - 4) = 0
:
y = +4 and y = -22
:
:
you can check both solutions in the distance equation;
They should = sqrt%28178%29