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:
By using the coordinates, we can reflect a given object about the x-axis, y-axis, line y = x, line y= x etc.
Solution;
Under reflection about x-axis,
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 y-axis,
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 x-axis,
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 x-axis
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 y-axis,
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 x-axis
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 y-axis
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 y-axis
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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Bibek
what is reflection?
Mar 24, 2017
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shivam
what is reflection
Jan 05, 2017
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