College Algebra, 2013a

168 Linear and Quadratic Functions
72. Show that if a ≠ b, the line containing the points (a, b) and(b, a) is perpendicular to the line
y = x. (Coupled with the result from Example 1.1.7 on page 13, wehavenowshownthatthe
line y = x is a perpendicular bisector of the line segment connecting (a, b) and(b, a). This
means the points (a, b) and(b, a) are symmetric about the line y = x. We will revisit this
symmetry in section 5.2.)
73. The function defined by I(x) =x is called the Identity Function.
(a) Discuss with your classmates why this name makes sense.
(b) Show that the point-slope form of a line (Equation 2.2) can be obtained from I using a
sequence of the transformations defined in Section 1.7.