Translation and Reflection of a Polygon

Oct 13, 2025 by miodeya.com 113 views

Translation and Reflection of a Polygon

In mathematics, a polygon is a two-dimensional shape with at least three straight sides and angles. When a polygon undergoes a translation, its position changes, but its size and shape remain the same. A reflection, on the other hand, is a transformation that flips the polygon over a line, called the line of reflection.

What is Translation in Mathematics?

Translation is a type of transformation that moves a polygon from one position to another without changing its size or shape. It is a movement of the polygon in a specific direction and distance. In the case of the given polygon, it is translated up eight units, which means that each vertex of the polygon is moved eight units upwards.

What is Reflection in Mathematics?

Reflection is a type of transformation that flips a polygon over a line, called the line of reflection. It is a mirror-like transformation that changes the position of the polygon. In the case of the given polygon, it is reflected across the x-axis, which means that each vertex of the polygon is flipped over the x-axis.

How to Translate a Polygon?

To translate a polygon, you need to add or subtract a specific value to the coordinates of each vertex. If the polygon is translated up, you add the value to the y-coordinate of each vertex. If the polygon is translated down, you subtract the value from the y-coordinate of each vertex.

How to Reflect a Polygon Across the X-Axis?

To reflect a polygon across the x-axis, you need to change the sign of the y-coordinate of each vertex. If the y-coordinate is positive, you change it to negative. If the y-coordinate is negative, you change it to positive.

Q&A

Q: What are the coordinates of the image of the polygon after translation and reflection?

A: To find the coordinates of the image of the polygon, we need to apply the translation and reflection transformations to each vertex of the polygon.

Q: How do we apply the translation transformation to the polygon?

A: We add 8 to the y-coordinate of each vertex to apply the translation transformation.

Q: How do we apply the reflection transformation to the polygon?

A: We change the sign of the y-coordinate of each vertex to apply the reflection transformation.

Q: What are the coordinates of the image of the polygon after translation and reflection?

A: Let's apply the translation and reflection transformations to each vertex of the polygon:

Vertex A (1, 5) becomes A' (1, 13) after translation and A'' (1, -13) after reflection.
Vertex B (3, -5) becomes B' (3, 3) after translation and B'' (3, -3) after reflection.
Vertex C (-4, -2) becomes C' (-4, 6) after translation and C'' (-4, -6) after reflection.
Vertex D (-6, 4) becomes D' (-6, 12) after translation and D'' (-6, -12) after reflection.
Vertex E (1, 8) becomes E' (1, 16) after translation and E'' (1, -16) after reflection.

Q: What is the shape of the image of the polygon after translation and reflection?

A: The shape of the image of the polygon remains the same after translation and reflection. The polygon is still a pentagon with five sides and angles.

Q: What is the size of the image of the polygon after translation and reflection?

A: The size of the image of the polygon remains the same after translation and reflection. The polygon is still the same size as the original polygon.

Conclusion

In this article, we discussed the translation and reflection of a polygon. We learned how to apply the translation and reflection transformations to each vertex of the polygon and how to find the coordinates of the image of the polygon after translation and reflection. We also answered some common questions about the translation and reflection of a polygon.