Let's work through the problems shown in the image.

1. Reflect Figure A over the x-axis and label the image B.

• To reflect a figure over the x-axis, we change the sign of the y-coordinate of each point on the figure, while keeping the x-coordinate the same.
• Suppose the vertices of triangle A have coordinates $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$. After reflection over the x-axis, the new coordinates would be $(x_1, -y_1)$, $(x_2, -y_2)$, and $(x_3, -y_3)$.

You can label the reflected triangle as Figure B.

2. Reflect Figure B over the y-axis and label the image C.

• To reflect a figure over the y-axis, we change the sign of the x-coordinate of each point, while keeping the y-coordinate the same.
• If the vertices of triangle B are $(x_1, -y_1)$, $(x_2, -y_2)$, and $(x_3, -y_3)$, after reflection over the y-axis, the new coordinates will be $(-x_1, -y_1)$, $(-x_2, -y_2)$, and $(-x_3, -y_3)$.

You can label this new figure as Figure C.

3. Are figures A and C congruent? Explain your thinking.

• Congruent figures have the same shape and size, but may be reflected, rotated, or translated. Since reflecting a figure over the x-axis and then the y-axis does not change the size or shape of the figure, Figures A and C are congruent. They are mirror images of each other, but their side lengths and angles remain unchanged.

Would you like more details on how to reflect points, or need further clarification on congruence?

5 Related Questions:

1. How do you determine the coordinates of a reflected point?
2. How does a reflection over the origin differ from a reflection over the x or y-axis?
3. Can reflecting a figure twice ever change its size or shape?
4. What are other types of transformations besides reflection?
5. Can two figures be congruent if one is rotated and the other is reflected?

Tip:

When reflecting over the x-axis or y-axis, always remember that only one coordinate changes (either x or y), not both!