Find the Coordinates of Point pDate: 10/22/2002 at 03:09:45 From: Erwin Schwarz Subject: Solving Radical Equations I'm trying to help my daughter with her Grade 11 math. The chapter is titled Solving Radical Equations and Inequalities, but I'm struggling with helping her on a particular question that goes like this: Point P lies on the line y=x. The coordinates of Q and T are (-1,8) and (8,1) respectively. The sum of the distances QP and TP is 18 units. Determine the coordinates of P. Date: 10/22/2002 at 12:07:39 From: Doctor Ian Subject: Re: Solving Radical Equations Hi Erwin, A picture usually helps: Q | P Q = (-1,8) | . | . | . | . T T = (8,1) ---------- -------------------- If the coordinates of P are (p,p) (it's on the line y=x, so the coordinates must have equal values), then QT = sqrt[(p - -1)^2 + (p - 8)^2] PT = sqrt[(p - 8)^2 + (p - 1)^2] (I just used the standard distance formula, distance from (x,y) to (x',y') = sqrt[(x - x')^2 + (y - y')^2] which can be derived from the Pythagorean Theorem.) And you're told that QT + PT = 18 The only thing that makes the problem workable is that you just have the one value, p, for both coordinates of P, since that gives you an equation in one variable. I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 10/22/2002 at 20:31:42 From: Erwin Schwarz Subject: Solving Radical Equations Yes, I see now, and to carry it further via substitution it becomes sqrt[(p-1)^2+(p-8)^2] + sqrt[(p-8)^2+(p-1)^2] = 18 and then you remove the radical by squaring both sides of the equation. Doesn't that leave the right side of the equation really messy, or am I missing some other form of reduction? P.S. Thanks for your help - this is an awesome webpage Date: 10/22/2002 at 22:37:50 From: Doctor Ian Subject: Re: Solving Radical Equations Hi Erwin, Yes, it's going to be a mess. I haven't worked it through to the end, but I'm guessing that you'll have to square the equation twice. It's easier to see why if we use simpler expressions: __ __ c = \| a + \| b __ __ c^2 = a + 2 \| a \| b + b ___ c^2 - a - b = 2\| ab (c^2 - a - b)^2 = 4ab Good luck! - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 10/23/2002 at 03:05:25 From: Erwin Schwarz Subject: Thank you (Solving Radical Equations) Excellent, I believe I can explain this to my daughter in such a way she will understand. Once again, this is an awesome service. Thank you. |
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