SOLUTION: i need your help: the abscissa of a point on the fourth quadrant is numerically 3 times its ordinate and is 10 units from (-2,4). find the point. i can't imagine this problem

Question 554022: i need your help:
the abscissa of a point on the fourth quadrant is numerically 3 times its ordinate and is 10 units from (-2,4). find the point.
i can't imagine this problem so i can't start solving it. i also don't know how to answer that one. please i need your help to answer that question... that really helps me a lot to understand the lesson involving that problem....
THANK YOU!!!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the abscissa of a point on the fourth quadrant is numerically 3 times its ordinate and is 10 units from (-2,4). find the point.
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Let the point be (x,y)
Equations:
x = 3y
10 = sqrt[(x+2)^2+(y-4)^2]
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Substitute for "x" and solve for "y":
10 = sqrt[(3y+2)^2 + (y-4)^2]
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100 = 9y^2+12y+4 + y^2-8y+16
10y^2+4y+20 = 100
5y^2 + 2y-40 = 0
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y = 2.6355 or y = -3.0355
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The 4th quadrant has y being negative and x being positive
But x = 3y implies that x and y have the same sign.
There is a contradiction here.
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If x = 2.6355, y = 7.9065 (this point would be in the 1st quadrant)
If x = -3.0355, y = -9.1065 (this point would be in the 3rd quadrant)
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Cheers,
Stan H.
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