$\"\"$

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a.

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Vertices of $\"\"$ are $\"\"$ and $\"\"$ .

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Find reflection along $\"\"$ -axis.

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Write the vertex matrix for $\"\"$ is $\"\"$ .

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To reflect the in the line $\"\"$ -axis, multiply the vertex matrix by $\"\"$

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$\"\"$ .

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Write the vertices of the image.

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The first row represents the $\"\"$ –coordinates and the second row represents the $\"\"$ –coordinates.

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The vertices are $\"\"$ and $\"\"$ . $\"\"$

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b.

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Graph:

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Plot the points $\"\"$ and $\"\"$ and connect the points to form $\"\"$ .

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Plot the points $\"\"$ and $\"\"$ and connect the points to form $\"\"$ .

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$\"\"$

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Observe the graph:

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$\"\"$ and $\"\"$ are similar, both has same shape. $\"\"$

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c.

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The points $\"\"$ and $\"\"$ are reflections of the points $\"\"$ and $\"\"$ across $\"\"$ –axis.

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$\"\"$ is a reflection of $\"\"$ across the $\"\"$ –axis.

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d.

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To reflect twice across $\"\"$ –axis, multiply the vertex matrix by the reflection matrix twice.

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The reflection matrix for reflection across $\"\"$ –axis is $\"\"$ .

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Multiply the reflection matrices are $\"\"$ .

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Multiplying a matrix by the identity matrix will give the same matrix.

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Thus, reflecting a triangle twice across the same line will produce the same matrix.

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$\"\"$

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a. Coordinates of the vertices of the images are $\"\"$ and $\"\"$ .

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b.Graph of the $\"\"$ and $\"\"$ is

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$\"\"$

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c. $\"\"$ is a reflection of $\"\"$ across the $\"\"$ –axis.

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d. Reflecting a triangle twice across the same line will produce the same matrix.