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May 30th, 2016, 02:35 PM  #1 
Senior Member Joined: Apr 2008 Posts: 193 Thanks: 3  how to find length MC in a rectangle length MC.pdf Please click the link above to see a diagram. The diagram shows a rectangle with vertices ABCD. M is a point inside the rectangle. AM is 3cm, BM is 12cm and DM is 11cm. Find the length of MC using coordinate geometry. Can someone please explain how to do it? Thank you very much. 
May 30th, 2016, 08:16 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,718 Thanks: 1806 
Express the squares of the distances in terms of the coordinates by use of Pythagoras. MC = 16cm (because 11² + 12² = 3² + 16²) 
May 30th, 2016, 08:20 PM  #3 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Let $\displaystyle D = (0,0)$, $\displaystyle M = (h, k)$, $\displaystyle B = (p, q)$. Then $\displaystyle \begin{cases} h^2 + k^2 = 11^2 = 121 & ...(1) \\ h^2 + (qk)^2 = 3^2 = 9& ...(2)\\ (ph)^2 + (qk)^2 = 12^2 = 144 & ...(3)\end{cases}$ And we need to find $\displaystyle \sqrt{(ph)^2 + k^2}$. $\displaystyle (1)  (2):\\ k^2  (qk)^2 = 112 ...(4) $ $\displaystyle (4) + (3):\\ (ph)^2 + k^2 = 256 = 16^2$ Thus $\displaystyle MC = 16$. 

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