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). Draw the triangle with vertices A(1, 1), B(4, 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.)

Answer 1

see below

Explanation:

Filling the given numbers into the given formulas, you have ...

Line AB:

x = 1 +(4-1)t, y = 1 +(3-1)t

x = 1+3t, y = 1+2t . . . . . . simplify

Line BC:

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

x = 4 -3t, y = 3 +4t . . . . . simplify

Line AC:

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

x = 1, y = 1+6t . . . . . . . . . .simplify