The parametric equations

$x=x_1(x_2-x_1)t,y=y_1(y_2-y_1)t$

where $0t1$ describe the line segment that joins the points $P_1(x_1,y_1^{\text{'}})$ and $P_2(x_2,y_2).$

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 $t.)$

$A$ to $B$

$B$ to $C$

$A$ to $C$

Find the distance traveled by a particle with position $(x,y)$ as $t$ varies in the given time interval.

$x=3si{n}^2(t),y=3co{s}^2(t),0t2$

What is the length of the curve?