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Math Help - Points (a, b) and (b, a)

  1. #1
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    Points (a, b) and (b, a)

    Show that the line containing the points (a, b) and (b, a),
    where a does not equal 0, 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
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    Show that the line containing the points (a, b) and (b, a),
    where a does not equal 0, is perpendicular to the line y = x.

    Also, show that the midpoint of (a, b) and (b, a) lies on the line y = x.
    The slope of y=x is 1.

    You'll need to find the slope of the segment between (a, b) and (b, a).

    m=\frac{y_2-y_1}{x_2-x_1}=\frac{a-b}{b-a}=\frac{-(b-a)}{b-a}=-1

    Since the slopes are negative reciprocals of each other, the lines are perpendicular.

    y=x is the linear identity function. this means the x and y values are identical.

    The midpoint between (a, b) and (b, a) can be found using the midpoint formula:

    M=\left(\frac{a+b}{2}, \frac{b+a}{2}\right)

    Since both x and y values of the midpoint are identical, then the midpoint has to lie on the identity function y=x
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  3. #3
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    Again...

    Quote Originally Posted by masters View Post
    The slope of y=x is 1.

    You'll need to find the slope of the segment between (a, b) and (b, a).

    m=\frac{y_2-y_1}{x_2-x_1}=\frac{a-b}{b-a}=\frac{-(b-a)}{b-a}=-1

    Since the slopes are negative reciprocals of each other, the lines are perpendicular.

    y=x is the linear identity function. this means the x and y values are identical.

    The midpoint between (a, b) and (b, a) can be found using the midpoint formula:

    M=\left(\frac{a+b}{2}, \frac{b+a}{2}\right)

    Since both x and y values of the midpoint are identical, then the midpoint has to lie on the identity function y=x
    Another educational reply.
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