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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

11.5 分比公式 Dividing Ratio Formula
11.5 Dividing Ratio Formula 分比公式


 

1. A(2, -3), B(h, k) and C(-3, 4) three points are located at the same straight line such that 5AB = 2BC. Find the values of h and k.

A(2, -3), B(h, k) 和 C(-3, 4) 三点在一条线上的点且5AB = 2BC. 求 h 和 k的.

Answer :
\frac{4}{7} , –1
2. P(5, p) separate the segment connecting A(3, 7) and B(6, 2) with ratio m : n. Find
P(5, p) 把连接 A(3, 7) 和 B(6, 2) 的线段分成比例 m : n. 求

(a) the ratio m : n,
比例 m : n

(b) the value of p.
p 的值。

Answer :
(a) 2 : 1

(b) 3\frac{2}{3}

3. Segment PQ is divided by point R externally such that RP = \frac{1}{2}RQ. If coordinates of Q and R are (8, -3) and (-16, 9) respectively, find the coordinate of P.

PQ 线段被点 R 外分使得 RP = \frac{1}{2}RQ. 若 Q 和 R 的坐标分别是 (8, -3) 和 (-16, 9), 求 P点的坐标.

Answer :
(–4, 3)
4. Points A(14, 6) and B(5, 11), given that the area of \bigtriangleupOAP is twice of the area of \bigtriangleupOPB where O is the origin and point P lies between A and B. Find the coordinate of point P.

点A(14, 6) 和 B(5, 11), 已知 \bigtriangleupOAP 的面积是 \bigtriangleupOPB 的两倍,其中 O 是原点且点 P 在 A 和 B 之间. 求点 P 的坐标.

Answer :
(8, 9\frac{1}{3})
5. Given the points A(-2, 1), B(3, 6). Find the point M which divides line AB in the ratio AM : MB = 3 : 2.

已知点 A(-2, 1), B(3, 6). 求把直线AB 分成AM : MB = 3 : 2 的点 M.

Answer :
(1, 4)
6. On a straight line A(-2,1) and B(2,7), find the coordinates of P if

在一直线上A(-2, 1)及B(2, 7), 求P之坐标, 若

(a) P divide AB into 3AP = 2PB internally

P內分直线AB成3AP = 2PB,

(b) P divide AB into 5AP = – AB externally

P外分直线AB成5AP = – AB,

Answer :

(a) \left(-\frac{2}{5} , \ 3\frac{2}{5})\right

(b) \left(-2\frac{4}{5} , \ -\frac{1}{5})\right

7. \bigtriangleupABC with vertices A(8, 10), B(0, -10) and C(12, -2), P and Q lie on AB and AC respectively. If PQ // BC, and the ratio of the area of \bigtriangleupAPQ to the area of \bigtriangleupABC is 1 : 16, calculate the coordinates of the midpoint of PQ.

\bigtriangleupABC之顶点A(8, 10), B(0, -10) 和C(12, -2), P 和Q 分別在AB 和AC上. 若PQ // BC, 且\bigtriangleupAPQ 和 \bigtriangleupABC 的面积比为1 : 16, 求PQ的中点座标.

Answer :
(7\frac{1}{2}, 6)
8. In \bigtriangleupABC, A(1, 2), B(9, 18) and C(13, -6). If P divide AB into 3 : 1 internally, Q on the segment AC and \bigtriangleupAPQ : \bigtriangleupABC = 1 : 2, find the coordinates of P, Q.

\bigtriangleupABC之顶点为A(1, 2), B(9, 18) 及C(13, -6). 若P內分AB之比为3 : 1, Q为线段AC上一点, 且\bigtriangleupAPQ : \bigtriangleupABC=1 : 2, 求P, Q之座标。

Answer :

(7, 14), (9, -3\frac{1}{3})