point of Division

Let the coordinates of C be (x1, y1) and the coordiantes of D be (x2, y2)

Since M is the intersection point of the two diagonals AC and BD,
M is the mid-point of AC and BD.

(-6 + x1) / 2 = 9
-6 + x1 = 18
x1 = 24

(-11 + y1) / 2 = 6
-11 + y1 = 12
y1 = 23

(7 + x2) / 2 = 9
7 + x2 = 18
x2 = 11

(5 + y2) / 2 = 6
5 + y2 = 12
y2 = 7

Therefore, the coordinates of C are (24, 23) and the coordinates of D are (11, 7)

If there is any mistake, please inform me.

2007-12-03 22:08:40 補充：
我用圖畫過, 答案是D = (11,7). 請問你所知的答案又是甚麼?謝謝!

2007-12-04 23:49:07 補充：
如果你嘗試繪畫A(-6,-11), B(7,5), C(24, 23) 和你的 D(11,-3), 你不能得到一個平行四邊形(parallelogram). 另一方面, 你可以檢查 slope of CD 是否和 slope of AB 相同. 明顯地, 用你的D(11,-3) 並不能得到和AB一樣的slope.我建議你檢查一下問題有沒有打錯.我會盡力幫你! 謝謝!

2007-12-04 23:53:01 補充：
如果你需要, 我send幅圖給你看來證實.

2007-12-05 22:47:32 補充：
AC and BD are diagonals. The mid-point of these two diagonals must coincide and that is M. If you still have questions, please feel free to ask.

2007-12-05 23:29:31 補充：
CORRECTION: =]Let the coordinates of C be (x1, y1) and the coordiantes of D be (x2, y2)(7 + x2) / 2 = 9 7 + x2 = 18x2 = 11(15 + y2) / 2 = 615 + y2 = 12y2 = -3Therefore, the coordinates of C are (24, 23) and the coordinates of D are (11, -3)

2007-12-05 23:48:14 補充：
題目所指的diagonals必須是AC跟BD. 這是因為一個平行四邊形的四點會順序為A, B, C, D. diagonal 對角線一定只會是AC和BD. 題目中的midpoint是指 AC 和 BD 的共同 midpoint. 因為一個平行四邊形一對對角線的midpoint是同一點.如果仍然不明白, 歡迎提問.

2007-12-06 23:29:39 補充：
我upload了一幅圖, 希望幫到你.http://i256.photobucket.com/albums/hh172/hkchelsea_united/question071202.png

2007-12-08 02:27:11 補充：
不一定要繪圖才較易, 因為我在答你的題目時, 是先打完回答, 之後才繪簡圖去肯定. 當然繪了圖會較易明白. 最緊要你記住平行四邊形的特性, 如對角線平分(diagonals bisect each other), 你便會記得此題的M必然是兩條對角線的中點(mid-point). 另外要留意是, 如果題目寫明是parallelogram ABCD, 則會有以下結論:1) AB//CD2) AD//BC3) AC and BD are diagonals <-- (此題用了這個特性)如果仍然有問題, 歡迎提出. (不過, 補充的次數有限, 如果仍然有問題, 歡迎電郵通知)