HELP!!!!!!!!數學幫幫手!!!!

2011-10-01 10:23 am
PQRS is a parallelogram with vertices P=(0,0),Q=(a,b) and S=(-b,a),FIND R
A:(-a,-b)
B:(a,-b)
C:(a-b,a-b)
D:(a-b,a+b)
E:(a+b,a+b)

要有STEP!!!!!!!!!THXXX

或者講解點解咁計THXXXX

回答 (1)

2011-10-01 10:48 am
✔ 最佳答案
Let(h, k) be the coordinates of R.

PR and QS are the diagonals of the parallelogram PQRS.
The mid-point of QS = ((a - b)/2, (a + b)/2)
The diagonals of a parallelogram bisect each other.
Hence, ((a - b)/2, (a + b)/2) is also the mid-point of PR.

Calculate the mid-point of PR :
(0 + h)/2 = (a - b)/2 and (0 + k)/2 = (a + b)/2
h = a - b and k = a + b
Hence, the coordinates of R = (a - b, a + b) ...... The answer is D.
參考: 土扁


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