Given:
A line segment with initial point (–5, 3) and terminal point (1, –6).
To find:
The set of parametric equations over the interval 0 ≤ t ≤ 1 which defines the given line segment.
Solution:
Initial point is (–5, 3). So,
[tex]x(0)=-5,y(0)=3[/tex]
Terminal point is (1, –6).
[tex]x(1)=1,y(1)=-6[/tex]
Check which of the given set of parametric equations satisfy [tex]x(0)=-5,y(0)=3,x(1)=1,y(1)=-6[/tex].
Put t=1 in each set of parametric equations.
In option A,
[tex]y(1)=3-6(1)=3-6=-3\neq -6[/tex]
So, option A is incorrect.
In option B,
[tex]y(1)=1-6(1)=1-6=-5\neq -6[/tex]
So, option B is incorrect.
In option C,
[tex]y(1)=3-9(1)=3-9=-6[/tex]
[tex]x(1)=-5+6(1)=-5+6=1[/tex]
Put t=0, in this set of parametric equations.
[tex]x(0)=-5+6(0)=-5[/tex]
[tex]y(0)=3-9(0)=3[/tex]
So, option C is correct.
In option D,
[tex]y(1)=1-7(1)=1-7=-3\neq -6[/tex]
[tex]x(1)=-5+8(1)=-5+8=3\neq 1[/tex]
So, option D is incorrect.
