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Math Help - Line Prove

  1. #1
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    Line Prove

    Show that the line containing the point (a, b) and (b, a) is perpendicular to the line y = x.

    Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.
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  2. #2
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    Hello, symmetry!

    I must assume that you are familiar with the basic concepts needed:
    . . slopes, perpendicular slopes, midpoints.

    If you are not, learn or re-learn the formulas and concepts.


    Show that the line containing the points (a, b) and (b, a)
    is perpendicular to the line: y = x

    The slope of the line through (a,b) and (b,a) is: . m_1 \:=\:\frac{a-b}{b - a} \:=\:-1

    The slope of the line y\:=\:x is: . m_2 = 1


    Since m_1\!\cdot\!m_2 \:=\:(-1)(1) \:=\:-1,\;\;m_1 \perp m_2



    Show that the midpoint of (a, b) and (b, a) lies on the line y \:= \:x

    The midpoint is: . \left(\frac{a+b}{2},\,\frac{a+b}{2}\right)

    The two coordinates of the midpoint are equal.
    . . Therefore, they satisfy the equation y \:=\:x

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  3. #3
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    ok

    I greatly appreciate your replies and detail explanation.
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