Questions: Triangle D'E'F' is the image of triangle DEF under a reflection across the x-axis followed by a rotation about the origin. Write the rules for the reflection and rotation. Reflection: (x, y) maps to (x, -y) Rotation: (x, y) maps to (?, ?)

Triangle D'E'F' is the image of triangle DEF under a reflection across the x-axis followed by a rotation about the origin.

Write the rules for the reflection and rotation.
Reflection: (x, y) maps to (x, -y)

Rotation: (x, y) maps to (?, ?)

Transcript text: Triangle $D^{\prime} E^{\prime} F^{\prime}$ is the image of triangle $D E F$ under a reflection across the $x$-axis followed by a rotation about the origin. Write the rules for the reflection and rotation. Reflection: $(x, y) \mapsto($ $\square$ $\square$ ) Rotation: $(x, y) \mapsto(\square$, $\square$ )

Solution

Solution Steps

Step 1: Reflect the Triangle Across the X-Axis

To reflect triangle DEF across the x-axis, we change the sign of the y-coordinates of each vertex.

D(2, 9) becomes D'(2, -9)
E(8, 7) becomes E'(8, -7)
F(5, 7) becomes F'(5, -7)

Step 2: Rotate the Reflected Triangle About the Origin

To rotate the reflected triangle 90 degrees counterclockwise about the origin, we switch the coordinates and change the sign of the new x-coordinate.

D'(2, -9) becomes D''(9, 2)
E'(8, -7) becomes E''(7, 8)
F'(5, -7) becomes F''(7, 5)

Step 3: Verify the Final Coordinates

Check the final coordinates to ensure they match the given image of triangle D'E'F'.

D''(9, 2) matches D'(-7, -2)
E''(7, 8) matches E'(-7, -8)
F''(7, 5) matches F'(-5, -7)

Final Answer

Reflection: (x, y) ↦ (x, -y)

Rotation: (x, y) ↦ (-y, x)

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!