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

Question

Quizplus · Accepted Answer

To find the parametric equations of the line segment, we need to first find the direction vector and a point on the line. We can use the two given points to find the direction vector.

Direction vector:
$$\vec{d}=\langle 12-(-3), -8-4\rangle=\langle 15,-12\rangle$$

A point on the line:
We can use either point, let's use $( - 3,4 )$.

Parametric equations:
If we let $( - 3,4 )$ be the initial point and $\langle 15,-12\rangle$ be the direction vector, the parametric equations are:
$$x = - 3 + 15 t$$
$$y = 4 - 12 t$$
We want to find the values of t that will give us the line segment. The segment starts at t = 0 when $( - 3,4 )$ is the point and ends at t = 1 when $(12,-8)$ is the point.
So, $$0 \leq t \leq 1$$ which is satisfied only by choice D.

Find Parametric Equations to Represent the Line Segment From (−3,4) to (12,−8)( - 3,4 ) \text { to } ( 12 , - 8 )(−3,4) to (12,−8)

Find Parametric Equations to Represent the Line Segment From $( - 3,4 ) \text { to } ( 12 , - 8 )$