Question

In Exercises \(23-28,\) find a parametrization for the curve. the ray (half line) with inith initial point \((-1,2)\) that passes through the point \((0,0)\)

Short answer

The parametrization for the curve is \(L(t) = (-1 + t, 2 - 2t)\)

Step-by-step solution

Understand the elements of the problem

The line begins at the point (-1,2), called the initial point, and passes through the original point (0,0). Our task is to find a parameterization for this line. A line can be parameterized as \(L(t) = (x_1, y_1) + t*(x_2 - x_1, y_2 - y_1)\) where (x_1, y_1) is the starting point, (x_2, y_2) is the second point, and t is the parameter.

Apply the formula to given points

Applying the formula, we get: \(L(t) = (-1, 2) + t*(0 - (-1), 0 - 2) = (-1, 2) + t*(1, -2)\)

Simplify the result

Our parameterization for the curve then simplifies down to \(L(t) = (-1 + t, 2 - 2t)\).