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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

12.4 两条直线的夹角 Angle Between Two Lines

12.4 Angle Between Two Lines 两条直线的夹角


 

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

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

Answer :
y = 3x – 9,5
(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。

Answer :
y = -2x + 13 , y = \frac{1}{2}x – 2
(3)
In an isosceles \bigtriangleupABC, 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\bigtriangleupABC, 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.

Answer :
y = \frac{1}{2}x – 2
(4)
In an equilateral \bigtriangleupABC, A(2, 3) and equation BC is x + y = 0. Find the equations of the other two sides.

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

Answer :
y = (2 \pm \sqrt3)x-1 \pm2\sqrt3)
(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.

Answer :
x – 7y + 40 = 0