Suppose parametric equations for the line segment.....

Question

Suppose parametric equations for the line segment between (8,-2) and (9,-2) have the form:

{x(t)=a+bt

{y(t)=c+dt

 

If the parametric curve starts at (8,-2) when t=0 and ends at (9,-2) at t=1, then find a,b,c, and d. 

a= 

b=

c=

d=

 

Answer 1

You have 4 unknowns, so you need 4 independent equations.  Knowing t at each end point, you can write 2 equations at each end point (one for the x value and one for the y value).

 

At (8,-2), t = 0:

 

8 = a + bt = a + b(0) ⇒

 

a = 8

 

-2 = c + dt = c + d(0) ⇒

 

c = -2

 

At (9,-2), t = 1:

 

9 = a + bt = 8 + b(1) ⇒

 

b = 1

 

-2 = c + dt = -2 + d(1) ⇒

 

d = 0

 

Test the answers.