Draw the triangle with vertices a(1, 1), b(5, 3), 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.)

Part A:

The parametric equations and where describes the line segment that joins the points and .

The parameterization of the line joining points A(1, 1) and B(5, 3) are given by substituting .

Thus, we have

x = 1 + (5 - 1)t = 1 + 4t
y = 1 + (3 - 1)t = 1 + 2t

Therefore, the parameterization of line joining points A(1, 1) and B(5, 3) are x = 1 + 4t and y = 1 + 2t.

Part B:

The parametric equations and where describes the line segment that joins the points and .

The parameterization of the line joining points B(5, 3) and C(1, 7) are given by substituting .

Thus, we have

x = 5 + (1 - 5)t = 5 - 4t
y = 3 + (7 - 3)t = 3 + 4t

Therefore, the parameterization of line joining points B(5, 3) and C(1, 7) are x = 5 - 4t and y = 3 + 4t.

Part C:

The parametric equations and where describes the line segment that joins the points and .

The parameterization of the line joining points C(1, 7) and A(1, 1) are given by substituting .

Thus, we have

x = 1 + (1 - 1)t = 1
y = 7 + (1 - 7)t = 7 - 6t

Therefore, the parameterization of line joining points A(1, 1) and B(5, 3) are x = 1 and y = 7 - 6t.