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In the x-y coordinate plane, the distance between (m, n) and (3, 4) is

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In the x-y coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]

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In the x-y coordinate plane, the distance between (m, n) and (3, 4) is\(√26\). If m and n are integers, how many possible cases are there?
A. 5 B. 6 C. 7 D. 8 E. 9
[Reveal] Spoiler: OA

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Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]

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==> From \((m-3)^2+(n-4)^2\)=(√26)2, you get (m-3, n-4)=(±1, ±5) or (±5, ±1), so there are total of 8 numbers. Therefore, the answer is D.

Answer: D
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Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]

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New post 20 Feb 2017, 18:48
I don't understand this question
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Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]

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Nunuboy1994 wrote:
I don't understand this question



    • The distance between any two points in a coordiante plane is given by -
      o \((x_1-x_2)^2 + (y_1-y_2)^2 = d^2\)
      o where \(d\) is the distance between the points (\(x_1,y_1\)) and (\(x_2,y_2\))
    • In the question, we are given that the distance between (\(m,n\)) and (\(3,4\)) is \(√26\)
    • Using the above formula, we can write -
      o \((m-3)^2 + (n-4)^2 = (√26)^2\)
      o \((m-3)^2 + (n-4)^2 = 26\)
    • Since m and n are integers, the value of \((m-3)^2\) and \((n-4)^2\) will also be integers.
      o We can write \((m-3)^2 + (n-4)^2 = 25 + 1\)
      o Now there are a number of possibilities - either
         \((m-3)^2 = 25\) and \((n-4)^2 = 1\)
         which gives us \(m-3 =\) +\(5\) or -\(5\) and \((n-4) =\)+\(1\)or -\(1\)
    • Thus from here we will get 2 possibilities of m and 2 possibilities of n. And the total number of cases possible are \(2 *2 = 4\)
OR
    • There is also a possibility that \((m-3)^2 = 1\) and \((n-4)^2 = 5\)
      o which gives us \(m-3 =\) +\(1\) or -\(1\) and \(n-4 =\) +\(5\) or -\(5\)
    • Thus, from here also there are 2 possibilities each for m and n. And the total number of cases possible are \(2 * 2 = 4\)
    • Therefore, the total number of cases possible for (\(m, n\)) are \(4 + 4 = 8\).

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Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is   [#permalink] 20 Feb 2017, 22:18
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