Questions: The endpoints of CD are C(1,2) and Translation: (x, y) -> (x+4, y) Reflection: in x-axis Reflection in y-axis Rotation: 90° about the origin

The endpoints of CD are C(1,2) and Translation: (x, y) -> (x+4, y) Reflection: in x-axis Reflection in y-axis Rotation: 90° about the origin
Transcript text: The endpoints of $\overline{C D}$ are $C(1,2)$ and Translation: $(x, y) \rightarrow(x+4, y)$ Reflection: in $x$-axis Reflection in $y$-axis Rotation: $90^{\circ}$ about the origin
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Solution

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Solution Steps

Step 1: Apply the translation

The initial point is C(1, 2). The translation rule is (x, y) → (x + 4, y). Applying this to C(1, 2) results in C'(1 + 4, 2) = C'(5, 2).

Step 2: Apply the reflection across the x-axis

Reflecting C'(5, 2) across the x-axis changes the sign of the y-coordinate. This gives C''(5, -2). This is plotted on the first graph shown.

Step 3: Apply the reflection across the y-axis

Reflecting C''(5, -2) across the y-axis changes the sign of the x-coordinate, resulting in C'''(-5, -2).

Final Answer:

The final coordinates after the sequence of transformations are (-5, -2).

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