Reflections Over The X-Axis, Y-Axis, and The Origin

TL;DR

Learn how to reflect points and graphs over the x-axis, y-axis, and origin.

Transcript

in this video we're going to focus on reflections specifically reflections over the x-axis the y-axis and the origin so let's take some notes let's start with reflections over the x-axis so let's say you have a point the ordered pair x y and you want to reflect that point over the x-axis the only thing you need to change is the Y value when you ref... Read More

Key Insights

• 💱 Reflection over the x-axis changes the Y values while keeping the X values the same.
• 💱 Reflection over the y-axis changes the X values while keeping the Y values the same.
• 💱 Reflection over the origin changes both the X and Y values.
• 📈 Reflecting a graph requires adjusting the equation or function accordingly.
• ❣️ The order of reflecting over the x-axis and y-axis affects the final position of the point or graph.
• ❣️ Reflecting over the origin involves a double reflection over the x-axis and y-axis.
• 💱 The shape of a graph can change when reflecting over the x-axis or y-axis.

Questions & Answers

Q: What happens to the X and Y values when reflecting a point over the x-axis?

When reflecting a point over the x-axis, the X values stay the same, but the Y values change.

Q: How does a graph reflect over the y-axis?

When reflecting a graph over the y-axis, the X values change, but the Y values remain the same.

Q: What happens to the X and Y values when reflecting a point over the origin?

When reflecting a point over the origin, both the X and Y values change sign.

Q: Can you explain the process of reflecting a figure across the y-axis?

To reflect a figure across the y-axis, change the sign of the X values for each point and plot the new figure.

Q: How can you reflect a graph over the x-axis and get a new equation?

To reflect a graph over the x-axis, put a negative sign outside the function and change the Y-intercept accordingly.

Q: What happens when reflecting an object over the origin?

When reflecting an object over the origin, both X and Y values change sign.

Q: How do you reflect a figure across the x-axis?

To reflect a figure across the x-axis, change the sign of the Y values for each point and plot the new figure.

Q: How does reflecting a graph over the y-axis affect its shape?

Reflecting a graph over the y-axis flips it horizontally, changing its shape but keeping the Y values the same.

Summary & Key Takeaways

• Reflection over the X-axis: The X values stay the same, but the Y values change.

• Reflection over the Y-axis: The Y values stay the same, but the X values change.

• Reflection over the origin: Both X and Y values change sign.