Question

The parametric equations below describe the line segment that joins the points P1(x1,y1) and P2(x2,y2). Find parametric equations to represent the line segment from (-5, 7) to (1, -2).?

Answer 1

Answer:

$x=-5+2t$

$y=7-3t$

for 0≤t≥3

Step-by-step explanation:

Parametric equations are defined as:

$x=x_0+at$

$y=y_0+bt$

where x₀,y₀,a and b are constants and a≠0 described by slope b/a

We must determine the slope as :

$m=(y_2-y_1)/(x_2-x_1)=-3/2$

Therefore a=2 and b=-3

We can use a point. Lets use point 1 (-5,7)

Therefore

$x_0=-5, y_0=7$

Plug into eqeuations:

$x=-5+2t$

$y=7-3t$

We can test points by making t=0,1,2 to get a parameter or range:

for t=0:

$x=-3, y=7[tex]

Which is our first point

x=3:

[tex]x=1, y=-2$

Which is our second point therefore the parameter is 0≤t≥3

Therefore the parametric equations are:

$x=-5+2t$

$y=7-3t$

for 0≤t≥3