Question

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). use a graphing device to draw the triangle with vertices a(1, 1), b(3, 4), c(1, 7). find the parametrization, including endpoints, and sketch to check. (enter your answers as a comma-separated list of equations. let x and y be in terms of t.)

Answer 1

It is a bit tedious to write 6 equations, but it is a straightforward process to substitute the given point values into the form provided.

For segment ab. (x1, y1) = (1, 1); (x2, y2) = (3, 4).

... x = 1 + t(3-1)

... y = 1 + t(4-1)

ab = {x=1+2t, y=1+3t}

For segment bc. (x1, y1) = (3, 4); (x2, y2) = (1, 7).

... x = 3 + t(1-3)

... y = 4 + t(7-4)

bc = {x=3-2t, y=4+3t}

For segment ca. (x1, y1) = (1, 7); (x2, y2) = (1, 1).

... x = 1 + t(1-1)

... y = 7 + t(1-7)

ca = {x=1, y=7-6t}