General Form, Distances and Families of Lines

Name: General Form, Distances and Families of Lines
Author: StemPy Lab

The general equation Ax + By + C = 0 and its normal form. The distance from a point to a line and between parallel lines, and which side of a line a point is on. Families of lines through an intersection, and the shift of origin.

3 lessons, about 1 h 15 min3 simulations11 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
The general equation and the normal form
Every straight line has an equation $Ax + By + C = 0$ , even a vertical one. Its slope is $-\dfrac{A}{B}$ and its intercepts are $-\dfrac{C}{A}$ and $-\dfrac{C}{B}$ . The normal form $x\cos\alpha + y\sin\alpha = p$ gives the distance $p$ of the line from the origin.
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 25 min
Distance from a point to a line
The distance of $(x_1, y_1)$ from $Ax + By + C = 0$ is $\dfrac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$ . Parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$ are $\dfrac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$ apart. The sign of $Ax_1 + By_1 + C$ tells which side of the line the point is on.
1 simulation1 practice question1 Python program5 problems1 Python lab
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Lesson 3about 25 min
Families of lines and the shift of origin
All lines through the meeting point of $L_1 = 0$ and $L_2 = 0$ are $L_1 + kL_2 = 0$ . Three lines are concurrent when the meeting point of two of them lies on the third. Shifting the origin to $(h, k)$ replaces $x$ by $X + h$ and $y$ by $Y + k$ .
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
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Straight Lines: Timed Test

10 questions · 25 min

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General Form, Distances and Families of Lines

Course outline (3 lessons)

The general equation and the normal form

Distance from a point to a line

Families of lines and the shift of origin

Test Your Learning

Your teacher

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