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.)

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sqdancefan sqdancefan · Answer 1 · 2018-07-15T00:18:12+02:00

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}

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kobenhavn kobenhavn · Answer 2 · 2021-10-07T05:42:43+02:00

The parametrization is:

From [tex]a[/tex] to [tex]b: x=1+2t[/tex] and [tex]y=1+3t[/tex].

From [tex]b[/tex] to [tex]c: x=3-2t[/tex] and [tex]y=4+3t[/tex].

From [tex]a[/tex] to [tex]c: x=1[/tex] and [tex]y=1+6t[/tex].

The parametric equations are , [tex]x=x_1+(x_2-x_1)t, y=y_1+(y_2-y_1)t,[/tex] where [tex]0\leq t\leq 1[/tex].

[tex]a(1,1), b(3,4), c(1,7)[/tex]

[tex]a[/tex] to [tex]b: (x_1, y_1)=(1,1)[/tex] and [tex](x_2, y_2)=(3,4)[/tex]

So, [tex]x=1+(3-1)t[/tex] and [tex]y=1+(4-1)t[/tex]

So, [tex]x=1+2t[/tex] and [tex]y=1+3t,[/tex] where [tex]0\leq t\leq 1.[/tex]

[tex]b[/tex] to [tex]c: (x_1, y_1)=(3,4)[/tex] and [tex](x_2, y_2)=(1,7)[/tex]

So, [tex]x=3+(1-3)t[/tex] and [tex]y=4+(7-4)t[/tex]

So, [tex]x=3-2t[/tex] and [tex]y=4+3t[/tex], where [tex]0\leq t\leq 1[/tex].

[tex]a[/tex] to [tex]c: (x_1, y_1)=(1,1)[/tex] and [tex](x_2, y_2)=(1,7)[/tex]

So, [tex]x=1+(1-1)t[/tex] and [tex]y=1+(7-1)t[/tex]

So, [tex]x=1[/tex] and [tex]y=1+6t[/tex], where [tex]0\leq t\leq 1[/tex].

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