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.DD . MATHS ==vector
2007-03-10 8:19 am
回答 (3)
2007-03-11 7:22 am
✔ 最佳答案
(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.
參考: My Maths knowledge
2007-03-12 10:40 pm
厲害
2007-03-10 2:51 pm
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.
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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