Find parametric equations to represent the line segment from $( - 3,4 )$ to $( 12 , - 8 )$.
A) $x = - 3 - 15 t , y = 4 - 12 t , 0 \leq t \leq 1$
B) $x = - 3 - 15 t , y = 4 - 12 t , \quad 0 \leq t \leq 2$
C) $x = 8 - 15 t , \quad y = 4 - 12 t , \quad 0 \leq t \leq 2$
D) $x = - 3 + 15 t , \quad y = 4 - 12 t , \quad 0 \leq t \leq 1$
E) $x = 3 + 15 t , \quad y = 4 - 12 t , \quad 0 \leq t \leq 1$

Question

Quizplus · Accepted Answer

We can find the parametric equations using the formula:
$$x = x_0 + (x_1 - x_0)t$$
$$y = y_0 + (y_1 - y_0)t$$
where $(x_0,y_0)$ and $(x_1,y_1)$ are the coordinates of the endpoints of the line segment and $t$ varies from 0 to 1.
Plugging in the given coordinates, we get:
$$x = -3 + (12 - (-3))t = -3 + 15t$$
$$y = 4 + (-8 - 4)t = 4 - 12t$$
Thus, the correct choice is (D).

Find Parametric Equations to Represent the Line Segment From (−3,4)( - 3,4 )(−3,4)

Find Parametric Equations to Represent the Line Segment From $( - 3,4 )$