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 February 23rd, 2018, 12:19 AM #1 Newbie   Joined: Feb 2018 From: Afghanistan Posts: 17 Thanks: 0 Analytic geometry problem Given points A(-4,-4) B (-8,-2) and C(x,0) what is x A)If AC-CB has its greatest value B)If AC+CB has its smallest value
 February 23rd, 2018, 01:57 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond Using calculus, A) x = -12 and B) x = -20/3.
 February 23rd, 2018, 05:18 AM #3 Newbie   Joined: Feb 2018 From: Afghanistan Posts: 17 Thanks: 0 I haven't studied calculus yet; is there another way? Last edited by skipjack; February 23rd, 2018 at 09:28 AM.
 February 23rd, 2018, 09:12 AM #4 Newbie   Joined: Dec 2017 From: Spain Posts: 18 Thanks: 1 You can solve this problem with analytic geometry and a calculator: Using the distance formula (Pythagoras): d=(√((x2-x1)^2)+((y2-y1)^2) We have that the distances AC and CB are: AC=[√((x-(-4))^2)+(-4)^2]=[√(x^2)+8x+32] CB[√((x-(-8))^2)+(-2)^2]=[√(x^2)+16x+68] Hence: AC±CB=[√(x^2)+8x+32]±[√(x^2)+16x+68] which are two different functions. With the calculator, you can get the highest point of the one function and the lowest point of the other function: The results will be: Highest point: x = -12 Lowest point: x = -(20/3) Thanks from greg1313 Last edited by skipjack; February 23rd, 2018 at 09:31 AM.
 February 23rd, 2018, 09:37 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,644 Thanks: 2084 (B) It's easy to show that the line AB intersects the x-axis at (-20/3, 0), and that this is the point C. Thanks from greg1313

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