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point of Division

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發問:

Given that A(-6,-11) and B(7,5)are two vertices of a parallelogramABCD and the diagonals intersects each other at M(9,6).Find the coordinates of C and D. 更新: C啱..D錯..Y不是7 更新 2: d(11,-3) 更新 3: 唔好意思...maybe個陣計得太耐..隻眼花花 B(7,15)...其他冇錯.. 更新 4: 唔好意思...我有嘢想問...m係ac and dc的mid point?? 定係m係ac 的mid point??而m又係dc的mid point?? why ge?? 更新 5: 請問..若a在左上角..那麼b.c.d又在那兒呢?? 更新 6: 請問在做這些題目時..是否畫了圖就比較易做??

最佳解答:

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)

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