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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

12.3 两条直线的平行与垂直 Parallel and Perpendicular Between Two Lines

12.3 Parallel and Perpendicular Between Two Lines 两条直线的平行与垂直


 

(1) The lines \frac{x}{t}+\frac{y}{3}=1and 4x + 3y – 4 = 0 are parallel, find the value of t and the distance of the lines.

直线\frac{x}{t}+\frac{y}{3}=1和4x + 3y – 4 = 0互相平行, 求t之值及此二平行线之距离.

Answer :
2\frac{1}{4}, 1
(2)

Points A(-1, 4), B(2, 7), C and D(1, 0) are the vertices of a parallelogram. Point E lies on BC such that BE = \frac{1}{3}BC. The lines that parallel to y-axis is drawn from A, meet x-axis at N and from E, meet line CD at F.

点A(-1, 4), B(2, 7), C 和 D(1, 0) 是一平行四边形的顶点. 点 E 在BC上使得 BE = \frac{1}{3}BC. 从点A 画一直线平行于 y-轴, 交 x-轴于 N 且从 E, 交直线 CD 于 F.

(a) Calculate coordinate of C and E.
计算C 和 E 的坐标。

(b) Find the equation of line DC and determine coordinate of F.
求直线DC 的方程式和找出 F的坐标.

(c) Explain why AEFN is a parallelogram and calculate its area.
试解释为何AEFN 是一个平行四边形并计算其面积。

Answer :
(a) (4, 3), (2\frac{2}{3}, 5\frac{2}{3})

(b) y = x – 1, (2\frac{2}{3}, 1\frac{2}{3})

(c) 14\frac{2}{3} unit^2

(3)
A, B and C are three points on line 2y + x = 10 that meets y-axis at A with AB : BC = 3 : 2 and point C is (8, p). Find
A, B 和 C 是直线 2y + x = 10 上的三个点并交 y-轴于 A 使得 AB : BC = 3 : 2 且点 C 是 (8, p). 求

(a) coordinate of point A,
A 点坐标

(b) value p,
p 的值,

(c) coordinate of point B,
B 点坐标,

(d) equation of the line that passes through point C and perpendicular to AC.
经过点C 且与 AC 的直线方程式。

Answer :
(a) (0, 5)

(b) 1

(c) (4.8, 2.6)

(d) y = 2x – 15