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Math Help - Shear transformation problem

  1. #1
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    Shear transformation problem

    Hey,

    Need a hint for this one. I feel I am missing something simple.



    Triangle ABP is mapped onto triangle ABQ by a shear. The lines BP and AQ intersect at C. Given that BC:CP = 1:3, and that the area of triangle ACB is 2 sq. cm, find the area of,

    (a) Triangle ACP,
    (b) Triangle CPQ
    (c) Quadrilateral ABQP

    I have solved part B, using similar triangles, and ratio of area to square of corresponding sides, to get 18 sq cm.

    But I am foggy on the parts (b) and (c). I see that Triangle ABP and Triangle ABQ have the same area, under a shear transform with shear factor 3. How to proceed further?

    Thanks.
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  2. #2
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    shear tranformation

    Hi mathguy80,
    I do not know shear formation but can give help.
    starting with AB = 2. PQ =6 Area CPQ = 18 (9*2)
    altofACBonAB =2 2*2*1/2 =2
    Alt of CPQ on PQ = 6 6*6*1/2 =18
    PA = 8



    bjh
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  3. #3
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    Hey bjhopper,

    I don't follow how you arrived at AB = 2, Can you please clarify? Thanks.
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  4. #4
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    Hi mathguy80,
    Given area ofACB =2.Altitude of ACB on AB = a
    a*AB *1/2 =2 a*AB =4 a and AB are each 2


    bjh
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  5. #5
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    Hi bjhopper,

    Sorry if I am really dense today. But I still don't follow how, given altitude * AB = 4, leads to altitude and AB both equal to 2.

    Couldn't AB = 1, altitude = 4, (ie:- 1x4 = 4), or vice versa also satisfy the same condition?
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  6. #6
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    Hi math guy 80,
    You are right AB =1 or 2.In either case all required areas will be the same.


    bjh
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  7. #7
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    are the angles PAB and APQ right angles, or are they unknown?
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