Question

Reflect triangle ABC with respect to the x -axis and the y -axis. What are the vertices of triangle A′B′C′ ?

Answer 1

To reflect a point or a shape with respect to the x-axis, we need to keep the x-coordinate the same and change the sign of the y-coordinate. Similarly, to reflect with respect to the y-axis, we need to keep the y-coordinate the same and change the sign of the x-coordinate.

Triangle ABC has vertices A, B, and C. When we reflect these points with respect to the x-axis, the x-coordinates stay the same, but the y-coordinates change signs. So, A' is the reflection of A, B' is the reflection of B, and C' is the reflection of C.

To reflect a point with respect to the x-axis, we change the sign of the y-coordinate, so if a point has coordinates (x, y), its reflection with respect to the x-axis will have coordinates (x, -y).

Similarly, when we reflect these points with respect to the y-axis, the y-coordinates stay the same, but the x-coordinates change signs. So, A'' is the reflection of A', B'' is the reflection of B', and C'' is the reflection of C'.

Therefore, the vertices of triangle A'B'C' are A' = (x, -y), B' = (x, -y), and C' = (x, -y).