Find the parametrization for the curve.
-The line segment starting at $( - 3,2 )$ with $t = 0$ and ending at $( 9,22 )$ with $t = 4$
A) $x = 3 t - 3 , y = 5 t + 2$, for $0 \leq t \leq 4$
B) $x = 2 t + 5 , y = - 3 t + 3$, for $0 \leq t \leq 4$
C) $x = - 3 t + 3 , y = 2 t + 5$, for $0 \leq t \leq 4$
D) $x = 5 t + 2 , y = 3 t - 3$, for $0 \leq t \leq 4$

Question

Quizplus · Accepted Answer

To find the parametrization of the line segment, we use the formula $x = x_0 + (x_1 - x_0)t$ and $y = y_0 + (y_1 - y_0)t$, where $(x_0, y_0)$ is the starting point, $(x_1, y_1)$ is the ending point, and $t$ varies from 0 to 1. However, since $t$ varies from 0 to 4 in this case, we adjust the formula accordingly. The change in $x$ from $-3$ to $9$ over the interval from $0$ to $4$ is $9 - (-3) = 12$, so the rate of change per unit $t$ is $12/4 = 3$. Similarly, the change in $y$ from $2$ to $22$ is $22 - 2 = 20$, so the rate of change per unit $t$ is $20/4 = 5$. Thus, the parametrization is $x = 3t - 3, y = 5t + 2$, for $0 \leq t \leq 4$.

Find the Parametrization for the Curve (−3,2)( - 3,2 )(−3,2) With t=0t = 0t=0

Find the Parametrization for the Curve $( - 3,2 )$ With $t = 0$