Polygon abcd is plotted on a coordinate plane. if the polygon translates 3 units to the left and 1 unit down, the length of diagonal a'c' is units. if the polygon translates 3 units further to the left and four units down, the length of diagonal a'c' .

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.