$\"\"$

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Observe the table:

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Quadrilateral $\"\"$ vertices are $\"\"$ and $\"\"$ .

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Quadrilateral $\"\"$ vertices are $\"\"$ and $\"\"$ .

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a.

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Find coordinates of $\"\"$ .

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Step 1:

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Write a matrix equation.

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Let $\"\"$ and $\"\"$ represent the coordinates of $\"\"$ and $\"\"$ respectively.

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

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

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Step 2:

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Adding the translation matrix $\"\"$ .

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$\"\"$ .

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Add corresponding elements.

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$\"\"$ .

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Equate the corresponding elements first columns and solve for $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Step 3:

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Substitute $\"\"$ and $\"\"$ in second columns corresponding elements and solve for $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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The image vertex $\"\"$ is $\"\"$ .

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$\"\"$

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b.

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Find coordinates of $\"\"$ .

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Equate the corresponding elements third columns and solve for $\"\"$ and $\"\"$ in the equation (1).

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$\"\"$

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in third columns corresponding elements and solve for $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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The vertex $\"\"$ is $\"\"$ .`

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$\"\"$

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Chek solution for $\"\"$ and $\"\"$ -values.

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Equate the corresponding elements fourth columns and check for $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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Case (i):

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Multiply)

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$\"\"$ (Add: $\"\"$ )

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Case (ii):

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Multiply)

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$\"\"$ (Subtract: $\"\"$ )

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$\"\"$

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a.The image vertex $\"\"$ is $\"\"$ .

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b.The vertex $\"\"$ is $\"\"$ .