Algebra 1 (Reiny or Kuai)

Show that PQRS is a rectangle.
(P: (1,4); Q: (2,6); R: (8,3); S: (7,1)

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  1. I did this for you , it was #5 of

    Ok, once more, very simple:

    slope PQ = (6-4/(2-1) = 2
    slope QR = (6-3)/(2-8) = -3/5

    So there is no right angle at Q

    but a rectangle must have 4 right-angles
    I have shown that one of them is not, so there is no point to continue

    It is NOT a rectangle

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  2. P: (1,4); Q: (2,6); R: (8,3); S: (7,1)

    PQ = (6-4)/(2-1) = 2/1 = 2

    QR = (3-6)/(8-2) = -3/6 = -1/2

    RS = (1-3)/(7-8) = 2

    PS = (1-4)/(7-1) = -3/6 = -1/2

    The slopes of all of consecutive sides are negative reciprocals. Therefore, quadrilateral PQRS with 4 angles is a rectangle.

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  3. sorry about my arithmetic error

    when I copied your diagram to paper, I had point
    Q as (3,6) instead of (2,6)

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