12.4 Angle Between Two Lines 两条直线的夹角

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(1)
If A(0, 1) and B(4, 3), find the equation of the line passing through B, making 45 with AB and cut the y-axis at the negative part.
If this line cut the x-axis at C, find the area of ABC.

若点A(0, 1)及B(4, 3), 求经过B且与直线AB交45又与y轴交于负值的直线方程式.
若此直线交x轴于C, 求ABC的面积.

(2)
Given that the equation of the hypotenuse of an isosceles right angle triangle is 3x – y + 1 = 0, the coordinate of the right angle is (6, 1), find the equations of the other two sides.

已知一等腰直角三角形之斜边为3x – y + 1 = 0，直角之坐标(6, 1)，求二腰之方程式。

(3)
In an isosceles ABC, AB = AC also the equation of AB and BC are 2x – y + 2 = 0 and x + y + 1 = 0 respectively. The line AC passes through the point (4, 0), find the equation of AC.

在等腰ABC, AB = AC且AB及BC方程式分別为2x – y + 2 = 0及x + y + 1 = 0. 直线AC经过点 (4, 0), 求AC之方程式.

(4)
In an equilateral ABC, A(2, 3) and equation BC is x + y = 0. Find the equations of the other two sides.

在一等边ABC, A (2, 3)和BC方程为x + y = 0. 求另两边的方程式.

(5)
If y = 3x is the equation of the mirror that reflected the incident ray x + y = 8, find the equation of the reflection ray.

若y = 3x为镜子的方程式, 其入射线为x + y = 8 的光, 求反射光线的方程式.