Formulating 2D Line Equations Using Vector Methods

00:00 5 marks

Given a line in the plane defined by the point \(P(2,-3)\) and the direction vector \(\mathbf{v} = \langle 4,5 \rangle\), write the parametric equations for the line and then convert them into the symmetric form. Provide your answers clearly.

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Hint

Recall the point-direction form of a line: \(x = x_0 + at\) and \(y = y_0 + bt\); then eliminate \(t\) to obtain the symmetric form.

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Parametric: \(x = 2+4t, \; y = -3+5t\); Symmetric: \((x-2)/4 = (y+3)/5\).

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Formulating 2D Line Equations Using Vector Methods

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Formulating 2D Line Equations Using Vector Methods

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