College Algebra 9th txtbk

114 CHAPTER 2 GRAPHS
below the x axis coincide when the paper is folded along the x axis. To make the intuitive
idea of folding a graph along a line more concrete, we introduce two related concepts—
reflection and symmetry.
Z DEFINITION 1 Reflection
1. The reflection through the y axis of the point (a, b) is the point (a, b).
2. The reflection through the x axis of the point (a, b) is the point (a, b).
3. The reflection through the origin of the point (a, b) is the point (a, b).
4. To reflect a graph just reflect each point on the graph.
EXAMPLE 3
Reflections
In a Cartesian coordinate system, plot the point P (4, 2) along with its reflection through
(A) the y axis, (B) the x axis, (C) and the origin.
SOLUTION
y
5
C (4, 2)
B (4, 2)
5
5
x
A (4, 2) P (4, 2)
5
MATCHED PROBLEM 3
In a Cartesian coordinate system, plot the point P (3, 5) along with its reflection through
(A) the x axis, (B) the y axis, and (C) the origin.
Z DEFINITION 2 Symmetry
A graph is symmetric with respect to
1. The x axis if (a, b) is on the graph whenever (a, b) is on the graph—
reflecting the graph through the x axis does not change the graph.
2. The y axis if (a, b) is on the graph whenever (a, b) is on the graph—
reflecting the graph through the y axis does not change the graph.
3. The origin if (a, b) is on the graph whenever (a, b) is on the graph—reflecting
the graph through the origin does not change the graph.