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DSE 數學公式 (Maths Formula): Equation of Straight Lines 直線方程公式

Equation of Straight Lines

→ Slope = \frac{y_2−y_1}{x_2−x_1} = tan θ

 

→ Equation :

1. y − y_1 = m(x − x_1)

2. y = mx + c

3. \frac{x}{a} + \frac{y}{b} = 1 (🌟比較少用,可不記)

 

→ Parallel and Perpendicular

If L_1 // L_2, then m_1 = m_2

If L_1 ⊥ L_2, then m_1 × m_2 = −1

 

→ Distance between two points : \sqrt{(x_1 − x_2)^2 + (y_1 − y_2)^2}

 

→ Mid-point = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})

 

→ Section formula : C = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n} )

 

→ Intersection between two lines :

For y = m_1x + c_1 and y = m_2x + c_2

Number of intersection Condition
1 m_1 ≠ m_2
0 m_1 = m_2 , c_1 ≠ c_2
Infinite many m_1 = m_2 , c_1 = c_2

 

→ Short Cut (記唔到可以唔記)

For Ax + By + C = 0

x-intercept = − \frac{C}{A}     /     Put y = 0

y-intercept = − \frac{C}{B}     /     Put x = 0

Slope = − \frac{A}{B}     /     Change to y = mx + c, m is the slope

 

 

直線方程公式

→ 斜率 = \frac{y_2−y_1}{x_2−x_1} = tan θ

 

→ 方程:

1. y − y_1 = m(x − x_1)

2. y = mx + c

3. \frac{x}{a} + \frac{y}{b} = 1 (🌟比較少用,可不記)

 

→ 平行及垂直

L_1 // L_2 , 則 m_1 = m_2

L_1 ⊥ L_2 , 則 m_1 × m_2 = −1

 

→ 兩點距離:\sqrt{(x_1 − x_2)^2 + (y_1 − y_2)^2}

 

→ 中點 = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})

 

→ 截點公式:C = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n})

 

→ 兩線之間的交點:

對於 y = m_1x + c_1y = m_2x + c_2

相交點數量 條件
1 m_1 ≠ m_2
0 m_1 = m_2 , c_1 ≠ c_2
無限 m_1 = m_2 , c_1 = c_2

 

→ Short Cut (記唔到可以唔記)

對於 Ax + By + C = 0

x截距 = − \frac{C}{A}     /     Put y = 0

y截距 = − \frac{C}{B}     /     Put x = 0

斜率 = − \frac{A}{B}     /     轉為 y = mx + c , m 為斜率

Equation of Straight Lines 直線方程課程

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