Il piano cartesiano
Scopri ed esplora il legame tra la posizione di un punto nel piano cartesiano e le sue coordinate, quindi rispondi alle domande visualizzate di seguito.
Ora tocca a te...
Il punto [math]P[/math] si trova nel primo quadrante, il punto [math]S[/math] nel secondo quadrante, il punto [math]T[/math] nel terzo quadrante e il punto [math]Q[/math] nel quarto quadrante.[br]Scrivi le possibili coordinate di questi punti.
Il punto [math]M[/math] e il punto [math]N[/math] hanno la stessa ordinata, uguale a [math]3,14[/math].[br]Come descriveresti la loro posizione nel piano cartesiano?
Qual è il valore dell'ascissa di un punto appartenente all'asse [math]y[/math]?[br]E quello dell'ordinata di un punto appartenente all'asse [math]x[/math]?
Scrivi le coordinate dei punti in figura.[br][br][img]data:image/png;base64,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[/img]
Retta per due punti - Coefficiente angolare
Grafico di una retta e coefficiente angolare
Il grafico descritto da una equazione nella forma [math]y=mx+q[/math] è una [i]retta,[/i] quindi una linea. [br]Ecco perchè tutte le funzioni di questo tipo si chiamano [i]funzioni lineari[/i].[br][br]Se conosciamo le coordinate di due punti della retta, [math]P_1=\left(x_1,y_1\right)[/math] e [math]P_2=\left(x_2,y_2\right)[/math] possiamo calcolare la [i]pendenza[/i] o [i]coefficiente angolare[/i] [math]m[/math] della retta: [math]m=\frac{y_2-y_1}{x_2-x_1}[/math]. [br]Tale valore è costante: comunque scegli due punti appartenenti alla fretta, il valore di [i]m[/i] è sempre lo stesso.
Ora prova tu...
Nell'app che segue, muovi i punti [math]A[/math] e [math]B[/math], quindi inserisci il valore della pendenza [math]m[/math] della retta che hai definito.[br]Seleziona [i]Verifica[/i] per scoprire se hai calcolato correttamente la pendenza e visualizzare la soluzione di questo esercizio.
Quando le cose non funzionano algebricamente...
Se hai una retta nella forma [math]f\left(x\right)=mx+q[/math] e/o le coordinate di due dei sui punti, [math]P_1=\left(x_1,y_1\right)[/math] e [math]P_2=\left(x_2,y_2\right)[/math] puoi calcolare: [br]- il valore [math]q[/math] dell'intersezione del grafico con l'asse [i]y[/i][br]- il valore del coefficiente angolare (pendenza) [math]m[/math] utilizzando la formula [math]m=\frac{y_2-y_1}{x_2-x_1}[/math].[br][br]Muovi i punti [i]A[/i] e [i]B[/i] nell'app qui sopra, in modo da allinearli verticalmente.[br]Scoprirai qual è il problema a livello algebrico che viene generato da una configurazione dei punti di questo tipo.
... e geometricamente
Muovi i punti [i]A[/i] e [i]B[/i] nell'app qui sopra, in modo da allinearli verticalmente.[br]Osserva il grafico della retta.[br]Questo è il grafico di una [i]funzione lineare[/i]?[br]Spiega le tue congetture.
Equazioni / Disequazioni 2° grado e parabole - Lezione+Esplorazione+Pratica
Risolvere graficamente le disequazioni di 2° grado
Il grafico di una [i][color=#1e84cc][b]funzione di 2° grado (quadratica)[/b][/color][/i] in un riferimento cartesiano ortogonale è una [i][color=#1e84cc][b]parabola[/b][/color][/i].[br][br]Per [i][b][color=#1e84cc]risolvere graficamente[/color][/b][/i] una [i][b][color=#1e84cc]disequazione di 2° grado [math]ax^2+bx+c>0[/math][/color][/b][/i] o [math]ax^2+bx+c<0[/math], traccia il grafico della parabola corrispondente, quindi:[br][list][*]Le [color=#1e84cc][i][b]ascisse[/b][/i][/color] dei punti (se esistono) in cui la [i][b][color=#1e84cc]parabola interseca[/color][/b][/i] l'[color=#1e84cc][i][b]asse x[/b][/i][/color] sono la [i][b][color=#1e84cc]soluzione[/color][/b][/i] dell'[color=#1e84cc][i][b]equazione[/b][/i][/color] [math]ax^2+bx+c=0[/math] (zeri dell'equazione)[/*][/list][list][*]Le [color=#1e84cc][i][b]ascisse[/b][/i][/color] dei punti (se esistono) in cui la [i][b][color=#1e84cc]parabola[/color][/b][/i] si trova[color=#1e84cc] [i][b]sopra[/b][/i][/color][i][b] [/b][/i]all'[color=#1e84cc][i][b]asse x[/b][/i][/color] sono [i][b][color=#1e84cc]soluzione[/color] [/b][/i]della [i][b][color=#1e84cc]disequazione [math]ax^2+bx+c>0[/math][/color][/b][/i] [/*][/list][list][*]The[color=#1e84cc] [/color][color=#1e84cc][i][b]ascisse[/b][/i][/color] dei punti (se esistono) in cui la [i][b][color=#1e84cc]parabola[/color][/b][/i][i][b][color=#1e84cc][/color][/b][/i] si trova[color=#1e84cc] [i][b]sotto [/b][/i][/color]all'[color=#1e84cc][i][b]asse x[/b][/i][/color] sono [i][b][color=#1e84cc]soluzione[/color] [/b][/i]della [i][b][color=#1e84cc]disequazione[/color][/b][/i][color=#1e84cc][i][b][/b][/i][/color] [math]ax^2+bx+c<0[/math][/*][/list]
Ora prova tu...
Determina graficamente le soluzioni di una equazione o disequazione di 2° grado, esplorando il grafico della parabola corrispondente.[br][br]Inserisci l'espressione nel campo di inserimento, quindi seleziona nell'elenco a discesa il verso della disequazione.[br][br]Utilizza la rotellina del mouse o i gesti predefiniti per i dispositivi mobili per fare uno zoom della vista Grafici e visualizzare meglio i dettagli, se necessario.[br]
Oggi l'insegnante sei tu!
Assegni in verifica la disequazione [math]x^2-49<0[/math]. [br][br]Alice la risolve così: [math]x^2<49\rightarrow x<\pm7[/math].[br][br]Bob risolve prima l'equazione [math]x^2-49=0[/math], e ottiene [math]x=\pm7[/math]. poi traccia un grafico della parabola corrispondente all'equazione e ottiene la soluzione [img]data:image/png;base64,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[/img].[br][br]Chad usa ChatGPT 2 e ottiene la soluzione [math]-7\le x\le7[/math].[br][br]Alice dice che il suo metodo è più veloce di quello di Bob, perchè non richiede neanche di disegnare grafici.[br][br]Correggi le verifiche dei tuoi studenti, e giustifica i voti assegnati.
Dubbio amletico...
Solo una tra le seguenti disequazioni ha per soluzione l'intervallo in figura. Quale?[br][img]data:image/png;base64,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[/img]
Ellisse come luogo geometrico
Esplora la costruzione di un'ellisse, come luogo geometrico dei punti del piano che godono tutti di una stessa proprietà.[br][br]Utilizza i dati numerici presenti nell'attività per determinare l'equazione dell'ellisse visualizzata.
Costruzione unitaria di ellisse, iperbole e circonferenza
Posiziona i fuochi[color=#9900ff] [i]F[/i][sub]1[/sub][/color]ed [color=#9900ff][i]F[/i][sub]2[/sub][/color] che determinano l'asse focale della conica da generare, imposta lo slider [color=#1551b5][i]asseM[/i][/color] che è la lunghezza dell'[color=#1e84cc][i]asse maggiore[/i][/color] della conica, quindi muovi il punto [i][color=#6aa84f]P[/color][/i] lungo la circonferenza per visualizzare il luogo geometrico.[br][br]La costruzione geometrica del luogo è la seguente:[br][list][*]Crea i due fuochi, [color=#9900ff][i]F[sub]1[/sub][/i][/color] ed [i][color=#9900ff]F[sub]2[/sub][/color][/i][br][/*][*]Traccia la circonferenza con centro in [color=#9900ff][i]F[/i][sub]1[/sub][/color] e [color=#1e84cc]raggio [i]r[/i] = [i]AsseM[/i][/color][/*][*]Preso un punto [color=#6aa84f][i]P[/i][/color] su di essa, traccia l’asse del segmento [i]P[/i][i]F[/i][sub]2[/sub][/*][*]La retta [i]P[/i][color=#ff0000][color=#000000][i]F[/i][/color][sub][color=#000000]1[/color] [/sub][/color]interseca l'asse nei punti [color=#1e84cc][i]L[/i][/color] della conica[/*][/list][br]Il punto [color=#0000ff][i]P[/i][/color], muovendosi sulla circonferenza, descrive il luogo dei punti[color=#1e84cc] [i]L[/i][/color], che è:[br][br]- un'[i]ellisse[/i] se [color=#9900ff][i]F[/i][sub]2[/sub][/color] è [i]interno [/i]alla circonferenza [i] distanza focale[/i] < [i]lunghezza asse[/i] → [i]e[/i] < 1[br][br]- un'[i]iperbole[/i] se [color=#9900ff][i]F[/i][sub]2[/sub][/color] è [i]esterno [/i]alla circonferenza [i]distanza focale[/i] > [i]lunghezza asse[/i] → [i]e[/i] > 1[br][br]- una[i] circonferenza[/i] se [color=#9900ff][i]F[/i][sub]1[/sub] ≡[i]F[/i][sub]2[/sub][/color] [i]distanza focale[/i] = 0 → [i]e[/i] = 0
Esplorazione del luogo
Dopo avere visualizzato la costruzione del luogo, disegna il triangolo [i]PLF[sub]2[/sub][/i] e rispondi alle seguenti domande.[br]
Che tipo di triangolo è [i]PLF[sub]2[/sub][/i] ?[br]Spiega.[br]
Scrivi la definizione canonica della conica visualizzata come luogo geometrico.
Utilizza le proprietà del triangolo [i]PLF[sub]2[/sub][/i] per dimostrare che il grafico ottenuto è proprio quello della conica.
Matrici e trasformazioni lineari
Seleziona un oggetto da trasformare (punto, retta, circonferenza, funzione, quadrato di lato unitario), quindi seleziona una trasformazione lineare.[br][br]Puoi esplorare le trasformazioni trascinando gli oggetti iniziali non vincolati a una definizione, che sono visualizzati in verde.[br]Gli oggetti trasformati sono visualizzati in rosso, ed essendo dipendenti dagli oggetti iniziali non possono essere trascinati.[br][br]Hai a disposizione alcune [color=#2980b9][i]trasformazioni predefinite[/i][/color]: le [color=#2980b9][i]simmetrie [/i][/color]rispetto agli assi cartesiani, gli [color=#2980b9][i]stiramenti[/i][/color], le [color=#2980b9][i]omotetie [/i][/color]e le [color=#2980b9][i]rotazioni[/i][/color].[br][br]In alternativa puoi selezionare una trasformazione [color=#2980b9][i]personalizzata[/i][/color], e definire la matrice della trasformazione [math]T=\begin{bmatrix} t_{11} & t_{12} \\ t_{21} & t_{22} \end{bmatrix} [/math] utilizzando gli slider visualizzati.
Esplora...
... come si fa?
Puoi utilizzare il calcolo matriciale per calcolare le coordinate dei punti trasformati di alcuni punti dati secondo una certa trasformazione individuata da una matrice [math]T[/math].[br][br]Se i punti assegnati hanno coordinate [math]\left(x_1,y_1\right),\left(x_2,y_2\right)[/math] e [math]\left(x_3,y_3\right)[/math], la matrice delle loro coordinate sarà [math]M=\begin{bmatrix} x_{1} & x_{2} & x_{3} \\ y_{1} & y_{2} & y_{3} \end{bmatrix} [/math], e la matrice delle coordinate dei punti trasformati sarà [math]M'=T\cdot M[/math].
... ora mettiti alla prova
Nell'app qui sopra, considera il quadrato unitario. Se consideriamo le coordinate dei suoi vertici in senso antiorario a partire dall'origine, possiamo costruire la matrice delle coordinate dei vertici: [math]M=\begin{bmatrix} 0 & 1 & 1 & 0\\ 0 & 0 & 1& 1 \end{bmatrix} [/math].[br][br]Ora seleziona una trasformazione [i]Personalizzata[/i], e poni uguale a 2 i due elementi della diagonale principale della matrice della trasformazione [math]T[/math], e uguale a 0 i due elementi della diagonale secondaria.[br]Che trasformazione hai ottenuto?[br]Confronta i valori dell'area del quadrato unitario e del quadrato trasformato.[br][br]E se avessi posto la matrice della trasformazione uguale a [math]T=\begin{bmatrix} 3 & 0 \\ 0 & 2 \end{bmatrix} [/math], quale sarebbe stata l'area della figura trasformata?[br][br]Verifica la tua congettura calcolando le coordinate dei vertici della figura trasformata e determinandone l'area.[br][br]
Manca una trasformazione?
Nell'elenco delle trasformazioni disponibili nell'app manca la [i]simmetria centrale[/i] di centro [math]O[/math].[br]Riesci a ottenere questa trasformazione utilizzando le opzioni disponibili?[br]Spiega la tua risposta in dettaglio.