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Math Help - Linear coordinate geometry

  1. #1
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    Linear coordinate geometry

    Hopefully this is the right section to be posting this...
    The point (h, k) lies on the the line y=x+1 and is 5 units from the point (0, 2). Write down two equations connecting h and k and hence find the possible values of h and k.
    Thanks in advance to anyone who can help.
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  2. #2
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    Since \displaystyle y = x + 1 and \displaystyle (h, k) lies on the line, that means \displaystyle k = h + 1.

    The distance from \displaystyle (h, h + 1) to \displaystyle (0, 2) is \displaystyle 5.

    So \displaystyle \sqrt{(h - 0)^2 + (h + 1 - 2)^2} = 5

    \displaystyle \sqrt{h^2 + (h - 1)^2} = 5

    \displaystyle \sqrt{h^2 + h^2 - 2h + 1} = 5

    \displaystyle \sqrt{2h^2 - 2h + 1} = 5

    \displaystyle 2h^2 - 2h + 1 = 25

    \displaystyle 2h^2 - 2h - 24 = 0

    \displaystyle 2(h^2 - h - 12) = 0

    \displaystyle h^2 - h - 12 = 0

    \displaystyle (h - 4)(h + 3) = 0

    \displaystyle h - 4 = 0 or \displaystyle h + 3 = 0

    \displaystyle h = 4 or \displaystyle h = -3.


    Since \displaystyle k = h + 1, that means the two possible values for \displaystyle (h, k) are \displaystyle (-3, -2) and \displaystyle (4, 5).
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  3. #3
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    Wow! You are brilliant. That makes perfect sense to me. Thanks so much.
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