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.