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標題:
A.DD . MATHS ==vector
發問:
ABCD is a quadrilateral .P, Q,R and S divide AB ,AD ,CD and CB respectively in the ratio 2:1 . a) Find the position vectors p, q, r ,s in terms of a, b,c,d. b) Prove that PQRS is a parallelogram.
(a) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazyvector41.jpg (b) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazyvector42.jpg Therefore PQRS is a parallelogram.
其他解答:
厲害|||||From the given conditions, AP=2PB AQ=2QD CR=2RD CS=2SB a. By proportions, p=((2*Xb+Xa)/3, (2*Yb+Ya)/3) q=((2*Xd+Xa)/3, (2*Yd+Ya)/3) r=((2*Xb+Xc)/3, (2*Yb+Yc)/3) s=((2*Xd+Xc)/3, (2*Yd+Yc)/3) b. By similar triangles, QP is parallel to DB, and RS is parallel to DB, Therefore QP is parallel to RS. Similarly PS is parallel to QR. Therefore PQRS is a parallelogram.
A.DD . MATHS ==vector
發問:
ABCD is a quadrilateral .P, Q,R and S divide AB ,AD ,CD and CB respectively in the ratio 2:1 . a) Find the position vectors p, q, r ,s in terms of a, b,c,d. b) Prove that PQRS is a parallelogram.
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最佳解答:(a) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazyvector41.jpg (b) 圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Crazyvector42.jpg Therefore PQRS is a parallelogram.
其他解答:
厲害|||||From the given conditions, AP=2PB AQ=2QD CR=2RD CS=2SB a. By proportions, p=((2*Xb+Xa)/3, (2*Yb+Ya)/3) q=((2*Xd+Xa)/3, (2*Yd+Ya)/3) r=((2*Xb+Xc)/3, (2*Yb+Yc)/3) s=((2*Xd+Xc)/3, (2*Yd+Yc)/3) b. By similar triangles, QP is parallel to DB, and RS is parallel to DB, Therefore QP is parallel to RS. Similarly PS is parallel to QR. Therefore PQRS is a parallelogram.
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