Rules
When reflecting a point over the x-axis, the new coordinates of the point (x₁,y) become (x₁,-y). On the other hand, when reflecting a point over the y-axis, the new coordinates (x,y) become (-x,y).
Notes/Examples
- A reflection is essentially a flip over a line called the line of reflection. Each point and its image are equidistant from the line of reflection, making reflection an example of a rigid motion.
- Common lines of reflection include the x-axis, y-axis, vertical or horizontal lines in the form X=#, and diagonal lines such as y=x.
Identifying the Line of Reflection
To identify the line of reflection, it is sometimes helpful to find the midpoint of the corresponding points.
Examples
- Triangle ABC with vertices A(-4, 2), B(4,7), and C(5, 1): When reflected over the x-axis, the new vertices become A'(-4,-2), B'(4,-7), and C'(5,-1).
- Rectangle PORS with vertices P(1, 2), Q(2, 5), R(8, 3), and S(7,0): When reflected over the y-axis, the new vertices become P'(-1,2), Q'(-2,5), R'(-8,3), and S'(-7,0).
Reflection over Other Vertical and Horizontal Lines
Reflecting in other vertical and horizontal lines has similar rules. For example, when reflecting in the line x = 4:
- Triangle JKL with vertices J(1, -1), K(2, 3), and L(3,-2) becomes J'(7,-1), K'(6,3), and L'(5,-2).
- Parallelogram CDEF with vertices C(-4,-4), D(-2, 0), E(6, 1), and F(4, -3) becomes C'(-2,-4), D'(-6,0), E'(6,-1), and F'(4,3).
More Examples
- Triangle XYZ with vertices X(-5, -2), Y(-3, 4), and Z(-1, 1) when reflected in the line y = x becomes X'(1,-5), Y'(4,-3), and Z'(1,-1).
- Square RSTU with vertices R(0, 3), S(5, 4), T(6,-1), and U(1, -2) when reflected in the line x= -1 becomes R'(-2,3), S'(-7,4), T'(-8,-1), and U'(-3,-2).
Identifying the Line of Reflection in More Examples
- Square ABCD with vertices A(-1, 3), B(0, 6), C(3, 5), and D(2, 2) when reflected in the line y = -x becomes A'(3,-1), B'(6,0), C'(5,3), and D'(2,2).
- Triangle STU with vertices S(-1,-6), 7(0, -3), and U(3,-4) when reflected in the line y = -x becomes S'(6,1), T'(3,0), and U'(4,-3).
By understanding and practicing the rules and examples of reflecting in vertical and horizontal lines, as well as identifying the line of reflection, students can gain a deeper comprehension of the topic through U9l2 reflections notes pdf and U9l2 reflections notes math.
