On the day after the fourth lecture of the year, random samples of 70 freshmen, 70 sophomores, 60 juniors, and 50 seniors were selected from the student body at the university, and each of these students was asked how many of the four lectures she had attended. Test that the number of lectures attended is independent of which year students are in.

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?