6.1 Required Independent Practice For this assignment, we are concerned with the movement of an object along a path in the plane. We are assuming that the plane is a coordinate plane and the object starts at the point ( 0, 0 ). As the object moves along the path each point on the path has two coordinates. The coordinates depend on the distance traveled along the path. Let us call this distance S. That is, S, is the length of the path from the origin ( 0,0 ), to a point P on the path as depicted in the figure 1. Evaluate the following a.) What value of S yields the coordinate point (2, 3)? S = 1 13 b.) What value of S yields the coordinate point (4, 4)? 3 = 13 + 1 + 5 2 c.) x (V13) = 2 d. ) y ( 1 + V13 ) = 3 e . ) x ( 2 ) = 1 .5 + f . ) y ( 4 ) = 2 . 5 (Challenge) Write explicit formulas (piecewise functions) describing the path of X(s) and Y(s). * y = $2x if 06X=2 y (s ) = 9 = 3 if 25 *43 fry = x if 34x4 4 2. Evaluate the following: a.) What value of S yields the coordinate point (2, 3)? + + S = 1 + JIO b.) What value of S yields the coordinate point (4, 3)? S = 3 + J10 C.) x (1 ) = 1 d. ) y ( 1 + v10 ) - 3 e . ) x ( 2 + V10 ) = 3 f . ) y ( 3 + V10 ) = 3 (Challenge) Write explicit formulas (piecewise functions) describing the path of X(s) and Y(s). O y=O if Ocx = 1 y (s ) = y= 3x - 3 if 15x=3 * (5 ) = y= 3 if 25 x = 4