$$\text { Find parametric equations to represent the line segment from } ( - 3,4 ) \text { to } ( 12 , - 8 ) \text {. }$$
A)$x = - 3 - 15 t , y = 4 - 12 t , 0 \leq t \leq 1$
B) $x = - 3 - 15 t , y = 4 - 12 t , 0 \leq t \leq 2$
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

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

Quizplus · Accepted Answer

We can find the direction vector of the line segment by subtracting the coordinates of the endpoints:
$$\langle 12,-8angle - \langle -3,4angle = \langle 15,-12angle$$
To parameterize the line segment, we can use the point-slope form of the equation of a line, with the endpoint $( - 3,4 )$ as the starting point and the direction vector $\langle 15,-12angle$:
$$\begin{aligned} x &= -3 + 15t \ y &= 4 - 12t \end{aligned}$$
To make sure the parameter $t$ covers the entire line segment from $( - 3,4 )$ to $( 12 , - 8 )$, we need $t$ to range from $0$ (corresponding to the starting point $( - 3,4 )$) to $1$ (corresponding to the ending point $( 12 , - 8 )$). Thus, the final answer is choice D with $0 \leq t \leq 1$.

Find parametric equations to represent the line segment from (−3,4) to (12,−8). \text { Find parametric equations to represent the line segment from } ( - 3,4 ) \text { to } ( 12 , - 8 ) \text {. } Find parametric equations to represent the line segment from (−3,4) to (12,−8).

$\text { Find parametric equations to represent the line segment from } ( - 3,4 ) \text { to } ( 12 , - 8 ) \text {. }$