About Lesson
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 :
, –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
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
3. Segment PQ is divided by point R externally such that RP = 
RQ. If coordinates of Q and R are (8, -3) and (-16, 9) respectively, find the coordinate of P.
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 = 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 
OAP is twice of the area of OPB where O is the origin and point P lies between A and B. Find the coordinate of point P.
OAP is twice of the area of OPB 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 OAP 的面积是 OPB 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)
)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)
*** QuickLaTeX cannot compile formula:
\left(-\frac{2}{5}
*** Error message:
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leading text: $\left(-\frac{2}{5}$
,
*** QuickLaTeX cannot compile formula:
\ 3\frac{2}{5})\right
*** Error message:
Missing delimiter (. inserted).
leading text: $\ 3\frac{2}{5})\right$
(b)
*** QuickLaTeX cannot compile formula:
\left(-2\frac{4}{5}
*** Error message:
Missing \right. inserted.
leading text: $\left(-2\frac{4}{5}$
,
*** QuickLaTeX cannot compile formula:
\ -\frac{1}{5})\right
*** Error message:
Missing delimiter (. inserted).
leading text: $\ -\frac{1}{5})\right$
7. ABC 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 APQ to the area of ABC is 1 : 16, calculate the coordinates of the midpoint of PQ.
ABC 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 APQ to the area of ABC is 1 : 16, calculate the coordinates of the midpoint of PQ.
ABC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APQ 和 ABC 的面积比为1 : 16, 求PQ的中点座标.
Answer :
(7, 6)
, 6)8. In ABC, A(1, 2), B(9, 18) and C(13, -6). If P divide AB into 3 : 1 internally, Q on the segment AC and APQ : ABC = 1 : 2, find the coordinates of P, Q.
ABC, A(1, 2), B(9, 18) and C(13, -6). If P divide AB into 3 : 1 internally, Q on the segment AC and APQ : ABC = 1 : 2, find the coordinates of P, Q.
ABC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APQ : ABC＝1 : 2, 求P, Q之座标。
Answer :
(7, 14), (9, -3)