SOLUTION: The abscissa of a point is two-fifths of its ordinate. Find the point if it is 5 units from (-2,2).

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Question 924394: The abscissa of a point is two-fifths of its ordinate. Find the point if it is 5 units from (-2,2).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that the point is (x,y).
"abscissa of a point is two-fifths of its ordinate"
x=%282%2F5%29y
Then use the distance formula,
%28x-%28-2%29%29%5E2%2B%28y-2%29%5E2=5%5E2
%28x%2B2%29%5E2%2B%28y-2%29%5E2=25
Substituting,
%28%282%2F5%29y%2B2%29%5E2%2B%28y-2%29%5E2=25
%284%2F25%29y%5E2%2B%288%2F5%29y%2B4%2By%5E2-4y%2B4=25
%2829%2F25%29y%5E2-%2812%2F5%29y%2B8=25
29y%5E2-60y%2B200=625
29y%5E2-60y-425=0
%28y-5%29%2829y%2B85%29=0
Two solutions:
y-5=0
y=5
Then,
x=%282%2F5%295=2
(2,5)
.
.
29y%2B85=0
29y=-85
y=-%2885%2F29%29
Then,
x=%282%2F5%29%28-%2885%2F29%29%29=-34%2F29
(-34/29,-85/29)
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