Course Content
第四章:部分分式 Partial Fraction
0/1
第六章:角的形成及单位 Angles and Measurements
0/1
第十三章: 方程组 Simultaneous Equations
0/1
第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
0/2
高中一 | 高级数学
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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
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