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

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(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.

(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 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 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

(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。

(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。