Reflections in Geometry: X and Y Axis Exploration

The video tutorial introduces the GeoGebra tool to visualize reflections on the coordinate plane. It explains how to reflect points over the x-axis and y-axis, using the axes as mirrors. The tutorial demonstrates the process with examples, showing how the coordinates change during reflection. Key rules for reflections are highlighted: over the x-axis, the x-coordinate remains the same while the y-coordinate becomes its opposite; over the y-axis, the y-coordinate stays the same while the x-coordinate becomes its opposite. The video emphasizes understanding the distance from the mirror and how it affects the reflected point.

What does the GeoGebra tool allow you to do with points on a coordinate plane?

• Measure their distance

• Calculate their area

• Determine their color

• Visualize their reflection

If a point is located at (3, 2) and is reflected over the x-axis, what will be its new coordinates?

• (-2, 3)

• (-3, 2)

• (2, 3)

• (3, -2)

What remains unchanged when a point is reflected over the x-axis?

• The x-coordinate

• None of the coordinates

• The y-coordinate

• Both coordinates

What happens to the y-coordinate of a point when it is reflected over the x-axis?

• It remains the same

• It doubles

• It becomes its opposite

• It becomes zero

According to the rules of reflection over the x-axis, if a point is at (-3, 4), where will its reflection be?

• (4, -3)

• (-3, -4)

• (3, 4)

• (-4, 3)

When reflecting a point over the y-axis, what remains constant?

• None of the coordinates

• Both coordinates

• The y-coordinate

• The x-coordinate

If a point at (-5, -2) is reflected over the y-axis, what will be its new coordinates?

• (5, -2)

• (-5, 2)

• (-2, -5)

• (2, 5)

What is the rule for the x-coordinate when reflecting a point over the y-axis?

• It becomes zero

• It becomes its opposite

• It doubles

• It remains the same

If a point is very close to the y-axis, what can be said about its reflection over the y-axis?

• It will also be very close

• It will be at the origin

• It will be on the y-axis

• It will be far away

What general observation can be made about the distance of a point from the y-axis and its reflection?

• The distance remains the same

• The distance halves

• The distance becomes zero

• The distance doubles