Exercises: Distances, parallel and perpendicular lines

Determine the equation of the line $g$ that is parallel to the line $h$ and passes through the point $P$ .

$h$ : $y = 3 x - 2$ ; $P(1|0) \;$

Für diese Aufgabe benötigst Du folgendes Grundwissen: Slope/Gradient of a line
$y = 3 x - 2$ ; $P (1 ∣ 0)$
For the line to be parallel to $h$ , it must have the same slope.
The slope of a line is the variable $m$ of the general line equation.
$m = 3$
Setting up the line equation
Plug $m = 3$ and $P (1 ∣ 0)$ into the the general line equation.
$\displaystyle 0$ $=$ $\displaystyle 3\cdot1+t$ $\displaystyle -3$
↓
solve for $t$
$\displaystyle t$ $=$ $\displaystyle -3$
Plug $m$ and $t$ into the general line equation.
$\;\;\Rightarrow\;\;$ Line equation: $y = 3 x - 3$
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$h$ : $y = x - 4$ ; $P(1|2) \;$

Für diese Aufgabe benötigst Du folgendes Grundwissen: Slope/Gradient of a line
$y = x - 4$ ; $P (1 ∣ 2)$
For the line to be parallel to $h$ , it must have the same slope.
The slope of a line is the variable $m$ of the general line equation.
$m = 1$
Setting up the line equation
Plug $m = 1$ and $P (1 ∣ 2)$ into the the general line equation.
$\displaystyle 2$ $=$ $\displaystyle 1+t$ $\displaystyle -1$
↓
solve for $t$
$\displaystyle t$ $=$ $\displaystyle 1$
Plug $m$ and $t$ into the general line equation.
$\Rightarrow\$ Line equation: $y = x + 1$
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$h$ : $y = 4 x$ ; $P(5|18) \;$

Für diese Aufgabe benötigst Du folgendes Grundwissen: Slope/Gradient of a line
$y = 4 x$ ; $P (5 ∣ 18)$
For the line to be parallel to $h$ , it must have the same slope.
The slope of a line is the variable $m$ of the general line equation.
$m = 4$
Setting up the line equation
Plug $m = 4$ and $P (5 ∣ 18)$ into the the general line equation.
$\displaystyle 18$ $=$ $\displaystyle 4\cdot5+t$ $\displaystyle -20$
↓
solve for $t$
$\displaystyle t$ $=$ $\displaystyle -2$
Plug $m$ and $t$ into the general line equation.
$\Rightarrow$ Line equation: $y = 4 x - 2$
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$h$ : $y = - 2 x + 1$ ; $P (- 1 ∣ 4)$

Für diese Aufgabe benötigst Du folgendes Grundwissen: Slope/Gradient of a line
$y = - 2 x + 1$ ; $P (- 1 ∣ 4)$
For the line to be parallel to $h$ , it must have the same slope.
The slope of a line is the variable $m$ of the general line equation.
$m = - 2$
Setting up the line equation
Plug $m = - 2$ and $P (- 1 ∣ 4)$ into the the general line equation.
$\displaystyle 4$ $=$ $\displaystyle −2⋅(−1)+t$ $\displaystyle -2$
↓
solve for $t$
$\displaystyle t$ $=$ $\displaystyle 2$
Plug $m$ and $t$ into the general line equation.
$\Rightarrow$ Line equation: $y = - 2 x + 2$
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$\displaystyle 0$	$=$	$\displaystyle 3\cdot1+t$	$\displaystyle -3$
	↓	solve for $t$
$\displaystyle t$	$=$	$\displaystyle -3$

$\displaystyle 2$	$=$	$\displaystyle 1+t$	$\displaystyle -1$
	↓	solve for $t$
$\displaystyle t$	$=$	$\displaystyle 1$

$\displaystyle 18$	$=$	$\displaystyle 4\cdot5+t$	$\displaystyle -20$
	↓	solve for $t$
$\displaystyle t$	$=$	$\displaystyle -2$

$\displaystyle 4$	$=$	$\displaystyle −2⋅(−1)+t$	$\displaystyle -2$
	↓	solve for $t$
$\displaystyle t$	$=$	$\displaystyle 2$

Setting up the line equation

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Setting up the line equation

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Setting up the line equation

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Setting up the line equation

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