Equazione esplicita di una retta dal grafico e della sua parallela e perpendicolare per un punto dato

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Irene Paniccia

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4 years, 10 months ago

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Irene Paniccia 4 years, 10 months ago

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Irene Paniccia 4 years, 10 months ago

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Irene Paniccia 4 years, 10 months ago

Created this as a copy of Equazione esplicita di una retta dato il grafico.

Name	Status	Author	Last Modified
Adrian's copy of Reading a graph of a function.	draft	Adrian Jannetta	16/08/2023 14:56
Function graph 1	draft	Adrian Jannetta	16/08/2023 14:56
Function graph 2	draft	Adrian Jannetta	16/08/2023 14:56
Polynomial Graph 1	draft	Adrian Jannetta	16/08/2023 14:56
Polynomial Graph 2	draft	Adrian Jannetta	16/08/2023 14:56
Graph 3 (Inverse function?)	draft	Adrian Jannetta	16/08/2023 14:56
Modulus graph (1)	draft	Adrian Jannetta	16/08/2023 14:56
Modulus graph (2)	draft	Adrian Jannetta	16/08/2023 14:56
Quadratic modulus graph	draft	Adrian Jannetta	16/08/2023 14:56
Trig transformation (1)	draft	Adrian Jannetta	16/08/2023 14:56
Trig transformation (2)	draft	Adrian Jannetta	12/01/2024 10:05
Straight line graph	draft	Adrian Jannetta	16/08/2024 10:02
Straight line graph	draft	Mark Hodds	08/09/2019 16:31
Polar graph (geogebra) #1	Should not be used	Adrian Jannetta	30/04/2024 13:53
Polar graph (geogebra) #2	draft	Adrian Jannetta	16/08/2023 14:56
Arnd's copy of Polar graph (geogebra) #1	draft	Arnd Ludwig	01/08/2018 12:36
Simple Harmonic Motion Graph	draft	Adrian Jannetta	16/08/2023 14:56
Shifted Simple Harmonic Motion Graph	draft	Adrian Jannetta	16/08/2023 14:56
JD's copy of Simple Harmonic Motion Graph	draft	JD Ichwan	21/05/2019 05:18
JD's copy of Polynomial Graph 2	draft	JD Ichwan	21/05/2019 05:32
JD's copy of Polynomial Graph 1	draft	JD Ichwan	21/05/2019 05:32
JD's copy of Function graph 1	draft	JD Ichwan	21/05/2019 05:41
Maria's copy of JD's copy of Function graph 1	draft	Maria Aneiros	25/05/2019 07:25
Maria's copy of JD's copy of Polynomial Graph 1	draft	Maria Aneiros	25/05/2019 07:25
Michael's copy of Trig transformation (1)	draft	Michael Proudman	07/12/2021 10:48
Tom's copy of Michael's copy of Trig transformation (1)	draft	Tom Bold	18/06/2019 14:00
Josh's copy of Trig transformation - simple geogebra	draft	Josh Lim	01/07/2019 12:35
StraightLine	Ready to use	Mario Orsi	26/03/2025 16:05
Equazione esplicita di una retta dal grafico e della sua parallela e perpendicolare per un punto dato	Ready to use	Irene Paniccia	25/05/2020 23:39
Rett linje	Ready to use	Elena Malyutina	26/08/2024 14:27

There are 55 other versions that do you not have access to.

Question statement

Il grafico che segue mostra la retta $r$ nel piano cartesiano e il punto $P$ a essa esterno.

{geogebra_applet('h46bjwqv', defs, [])}

Give any introductory information the student needs.

			Name	Type	Generated Value

defs	list	Nested 3×2 list
m0	rational	-2/3
q0	integer	3
P	vector	vector(-3,-2)
x_P	integer	-3
y_P	integer	-2
m	rational	-2/3
q	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[
  ['m',m],
  ['q',q],
  ['P',P]
]

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ [ "m", -2/3 ], [ "q", 3 ], [ "P", vector(-3,-2) ] ]

← Depends on:

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Statement

Parts

a) Gap-fill
1. Gap equazione Mathematical expression
  Add
b) Gap-fill
1. Gap x_P Number entry
  Add
2. Gap y_P Number entry
  Add
c) Gap-fill
1. Gap parallela Mathematical expression
  Add
d) Gap-fill
1. Gap perpendicolare Mathematical expression
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Qual è l'equazione della retta $r$?

$r : \, y = $ equazione

Advice

a) Per determinare l'equazione della retta $r$, osserviamo innanzitutto che, per ogni avanzamento di un'unità verso destra, la retta avanza di $\simplify[fractionNumbers]{{m}}$ in verticale. Dunque $m = \simplify[fractionNumbers]{{m}}$. Essendo l'intersezione con l'asse $y$ in $( 0 ; \var{q})$, si ha $q = \var{q}$.

In definitiva

\begin{equation} r : \, y = \simplify[zeroFactor,fractionNumbers,unitFactor]{{m} x+ {q}} . \end{equation}

b) Per determinare le coordinate del punto $P$, è sufficiente osservare il grafico: si ha $P = ({x_P};{y_P})$.

c) Il fascio (improprio) di rette parallele alla retta data ha equazione $y = \simplify[zeroFactor,fractionNumbers,unitFactor]{{m} x + q}$. Imponendo il passaggio di una retta del fascio per il punto $P$ otteniamo $q = \simplify[zeroFactor,fractionNumbers,unitFactor]{{y_P - m*x_P}}$.

Pertanto

\begin{equation} s : \, y = \simplify[zeroFactor,fractionNumbers,unitFactor]{{m} x + {y_P - m*x_P}} . \end{equation}

d) Il fascio (improprio) di rette perpendicolari alla retta data ha equazione $y = \simplify[zeroFactor,fractionNumbers,unitFactor]{{- 1/m} x + q}$. Imponendo il passaggio di una retta del fascio per il punto $P$ otteniamo $q = \simplify[zeroFactor,fractionNumbers,unitFactor]{{y_P + 1/m*x_P}}$.

Pertanto

\begin{equation} t : \, y = \simplify[zeroFactor,fractionNumbers,unitFactor]{{-1/m} x + {y_P +1/m*x_P}} . \end{equation}

Give a worked solution to the whole question.

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Part	Test	Passed?
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Gap-fill		Hasn't run yet
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This question is used in the following exam:

Verifica di Matematica - Classe II G by Irene Paniccia in Irene's workspace.

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Equazione esplicita di una retta dal grafico e della sua parallela e perpendicolare per un punto dato

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Irene Paniccia 4 years, 10 months ago

Irene Paniccia 4 years, 10 months ago

Irene Paniccia 4 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Error

Equazione esplicita di una retta dal grafico e della sua parallela e perpendicolare per un punto dato

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Irene Paniccia 4 years, 10 months ago

Irene Paniccia 4 years, 10 months ago

Irene Paniccia 4 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`