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Analitiese Meetkunde: Gradiënt lyn

Module by: Free High School Science Texts Project. E-mail the author

Berekening van die Gradiënt van 'n Lyn

Die gradiënt van 'n lyn beskryf hoe steil die lyn is, hoe groot die helling van die lyn is. In die figuur hieronder is lyn PTPT se helling die grootste. Lyn PSPS is minder steil as PTPT maar is steiler as PRPR, en die lyn PRPR is steiler as PQPQ.

Figure 1
Figure 1 (MG10C14_017.png)

Die gradiënt van die lyn word gedefinieer as die verhouding tussen die vertikale verandering in posisie en die horisontale verandering in posisie. Dit kan verstaan word deur te kyk na die lyn as die skuinssy van die reghoekige driehoek. Die gradiënt is die verhouding van die lengte van die vertikale sy van die driehoek tot die horisontale sy van die driehoek. Dink aan 'n lyn tussen punt AA met koördinate (x1;y1)(x1;y1) en punt BB met koördinate (x2;y2)(x2;y2).

Figure 2
Figure 2 (MG10C14_018.png)

Gradiënt=y2-y1x2-x1=y2-y1x2-x1

Ons kan gradiënt gebruik om te bepaal of twee lyne parallel is aan mekaar of loodreg is op mekaar. As die lyne parallel is (Figure 3a) sal hulle dieselfde gradiënt hê, byvoorbeeld mAB=mCDmAB=mCD. As hulle loodreg is op mekaar, (Figure 3b) dan sal: -1mAB=mCD-1mAB=mCD

Figure 3
Figure 3 (geom.png)

Byvoorbeeld, die gradiënt van die lyn tussen punt PP en QQ, met koördinate (2;1) en (-2;-2) ((Reference)) is:

Gradiënt = y 2 - y 1 x 2 - x 1 = - 2 - 1 - 2 - 2 = - 3 - 4 = 3 4 Gradiënt = y 2 - y 1 x 2 - x 1 = - 2 - 1 - 2 - 2 = - 3 - 4 = 3 4
(1)

Die volgende video bied 'n opsomming van die gradiënt van 'n lyn.

Figure 4
Gradiënt van 'n lyn

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