Reflection
Reflection
If we stand in front of a mirror, our images come closer to the mirror and vice versa, it is known as reflection. In reflection, the mirror is represented by a line, which is called the axis of reflection. The properties of reflection are:
 Lateral inversion of each other
 Equidistant from the mirror line
 Congruent to each other
Reflection using Coordinates
By using the coordinates, we can reflect a given object about the xaxis, yaxis, line y = x, line y= x etc.
 Reflection in Xaxis: When we reflect a point across the xaxis, the x coordinate remains the same, but y coordinate is transformed into negative.
The reflection of the point (x, y) across the xaxis is the point (x,−y).
P(x, y) → P'(x, y)
or, xaxis (x, y) = (x,−y)  Reflection in Yaxis: When we reflect a point across the yaxis, then y coordinator remains the same, but the x coordinate is transformed into negative.
The reflection of the point (x, y) across the yaxis is the point (−x, y).
P(x, y) → P'(−x, y)
or, yaxis (x, y) = (−x, y)  Reflecting in the line y = x: When we reflect a point across the line y = x, the x coordinate and then y coordinate change place.
The reflection of the point (x, y) across the line y = x is the point (y, x).
P(x, y) → P'(y, x)
or, y = x (x, y) = (y, x)  Reflection in line y = −x: When we reflect a point across the line y = −x, the x coordinate and then y coordinate change places and are negated or the signs are changes.
The reflection point (x, y) across the line y = −x is the point (−y,−x)
P(x, y) → P'(−y,−x)
 The reflection of the point (x, y) across the xaxis is the point (x, −y) = P(x, y) → P'(x, y)
 The reflection of the point (x, y) across the yaxis is the point (−x, y) = P(x, y) → P'(−x, y)
 The reflection of the point (x, y) across the line y = x is the point (y, x) = P(x, y) → P'(y, x)
 The reflection of the point (x, y) across the line y = −x is the point (−y, −x) = P(x, y) → P'(−y, −x)
Solution;
Under reflection about xaxis,
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) A(1, 3) \(\rightarrow\) A'(1, 3)
B(4, 5) \(\rightarrow\) B'(4, 5) and
C(6, 2) \(\rightarrow\) C'(6, 2)
\(\triangle\)ABC and its image \(\triangle\)A'B'C' are shown on the graph.
Solution;
Under reflection about yaxis,
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) A(2, 3) \(\rightarrow\) A'(2, 3)
B(4, 5) \(\rightarrow\) B'(4, 5) and
C(6, 2) \(\rightarrow\) C'(6, 2)
\(\triangle\)ABC and its image \(\triangle\)A'B'C' are shown on the graph.
Solution;
Under reflection about xaxis,
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) P(3, 1) \(\rightarrow\) P'(3, 1)
Q(5, 4) \(\rightarrow\) Q'(5, 4) and
R(2, 6) \(\rightarrow\) R'(2, 6)
\(\triangle\)PQR and its image \(\triangle\)P'Q'R' are shown on the graph.
Solution:
Under reflection about xaxis
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) A(4, 5) \(\rightarrow\) A'(4, 5) and
B(6, 2) \(\rightarrow\) B'(6, 2)
Line AB and its image A'B' are shown on the graph.
Solution;
Under reflection about yaxis,
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) X(1, 3) \(\rightarrow\) X'(1, 3) and
Y(4, 5) \(\rightarrow\) Y'(4, 5)
Line XY and its image X'Y' are shown on the graph.
Solution:
Under reflection about xaxis
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) A(5, 2) \(\rightarrow\) A'(5, 2) and
B(2, 3) \(\rightarrow\) B'(2, 3)
Line AB and its image A'B' are shown on the graph.
Solution:
Under reflection about yaxis
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) A(5, 2) \(\rightarrow\) A'(5, 2) and
B(2, 3) \(\rightarrow\) B'(2, 3)
Line AB and its image A'B' are shown on the graph.
Solution:
Let AB be the given point, then
A(3, 4) and B (8, 10)
Under reflection about yaxis
P(x, y) \(\rightarrow\) P'(x, y)
\(\therefore\) A(3, 4) \(\rightarrow\) A'(3, 4) and
B(8, 10) \(\rightarrow\) B'(8, 10)
line AB and its image A'B' are shown on the graph.

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