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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

12.5 两条直线的交点 Point of Intersection of Two Lines

12.5 Point of Intersection of Two Lines 两条直线的交点


 

(1)
Find the equation of the line with gradient –4 and passes through the intersection point of lines x +2y = 3 and 2x – 5y = 15.

求经过直线x +2y = 3 和 2x – 5y = 15的交点且斜率为 –4的直线方程式.

Answer:
4x + y – 19 = 0
(2)
An isosceles triangle ABC where AB = AC. Coordinates of point A and point B are (1, –5) and (5, 2) respectively. Given that the gradient of BC is \frac{2}{3} and the line perpendicular to BC and passes through A meet BC at D, find
一等腰三角形ABC 其中 AB = AC. 点 A 和点 B 的坐标分别是 (1, –5) 和 (5, 2). 已知 BC 的斜率是 \frac{2}{3} 且与 BC 垂直并经过 A 的直线交 BC 于 D, 求

(a) the equation of BC and equation of AD in general form,
BC 和 AD 的一般式方程式

(b) coordinate of points C and D,
点C 和D 的坐标

(c) length of AD.
AD 的长

Answer:
(a) 2x – 3y – 4 = 0, 3x + 2y + 7 = 0

(b) (–7, -6), (–1, –2)

(c) \sqrt{13} unit

(3)
Given that 3x + 2y + 9k = 0, 2x + y – 5 = 0, x + ky + 2 = 0 are concurrent, find the value of k

已知三条直线 3x + 2y + 9k = 0, 2x + y – 5 = 0, x + ky + 2 = 0 共点, 求k的值。

Answer:
–1, \frac{2}{3}
(4)
If the straight line x – ky + 1 = 0 passes through the intersection of the lines kx – y + 1 = 0 and y = x + 5, find the values of k.

若直线x – ky + 1 = 0 通过两直线kx – y + 1 = 0 与y = x + 5 的交点,试求k的值。

Answer:
1, -\frac{3}{5}