Distance Formula problem

ryan_kalle

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Jul 17, 2010
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College Algebra course. Instructor have us this assignment.

1. Let m and n be any real numbers. What is the distance between (0,0) and (2m, m^2 - 1)? What is the distance between (0,0) and (2mn, m^2 - n^2)?

I don't understand what exactly he is wanting. MY confusing is on the phrase "Let m and n be any real numbers."

"all real numbers" means (-infinity, infinity) but this says "any" do I get to just pick 2 random digits?
 
I assume you know the distance formula. m and n are any reals. This just means the formula works for any reals.

Just sub 2m and m^2-1 into the distance formula and simplify.

(2m0)2+(m210)2\displaystyle \sqrt{(2m-0)^{2}+(m^{2}-1-0)^{2}}

Do the same for the second part of the problem.
 
DistanceFormula (in the plane): d = (x2x1)2+(y2y1)2\displaystyle Distance Formula \ (in \ the \ plane): \ d \ = \ \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Hence, now knowing the distance formula, the rest should be elementary my dear Watson.\displaystyle Hence, \ now \ knowing \ the \ distance \ formula, \ the \ rest \ should \ be \ elementary \ my \ dear \ Watson.
 
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