Question

(a) Show that the parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1, describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). This answer has not been graded yet. (b) Find parametric equations to represent the line segment from (−2, 8) to (3, −2). (Enter your answer as a comma-separated list of equations. Let x and y be in term

Answer 1

Answer:

Step-by-step explanation:

a) First, we must check that at t =0, we get the point $(x_1,y_1)$ and at t=1 we get  $(x_2,y_2)$. Note that

$x_1+(x_2-x_1)\cdot 0 =x_1$

$y_1+(y_2-y_1)\cdot 0 =y_1$

$x_1+(x_2-x_1)\cdot 1 = x_2+x_1-x_1 = x_2$

$y_1+(y_2-y_1)\cdot 1 =y_2 + y_1 - y_1 = y_2$

Since in this case $x_1,x_2, y_1, y_2$ are all constants, we have that x and y are of the from $x= a+bt, y = c+dt$ for appropiate a,b,c,d. This functions are polynomials of degree one on the variable t, hence are continous over the interval $[0,1]$. This means, that they map continously al the points that lay on the line segment that joins $(x_1,y_1)$ and $(x_2,y_2)$.

b) We have that $x_1 = -2, x_2 = 3, y_1=8, y_2 = -2$, so the parametric equations are

$x = -2+(3-(-2))t = -2+5t$

$y =8+(-2-8)t = 8-10t$

Note that if t =0, we get the point (-2,8) and if t=1 we get $(-2+5,8-10) = (3,-2)$

Answer 2

Answer:

(3, - 2)

Step-by-step explanation:

Hope this helps