Reflecting over a vertical line

This will be a brief post. I continued with students trying to determine the relationship between reflected points and the line over which they points were reflected.

I encouraged students to write their results on the board (vertical line used, pre-image coordinates, image coordinates). After getting a half-dozen results on the board, I asked students to look for patterns and connections. Not much was happening, so I told students to get out of their seats and take a closer look for connections.

Students returned to their seats and some discussions began. Different students started interacting with other groups. Some students continued to try new values. I let the struggles continue and periodically asked what the connection was between the coordinates and the line used.

Finally, two girls went to the board on their own and were arguing/discussing the relationship. Their discussion centered on the idea of midpoints. After they had satisfied themselves, I asked the two to share their discussion with the rest of the class. There was a lot of discussion and questions about this idea, but gradually the class started to come together with the idea.

I checked their understanding by giving two x-coordinates and asking what line was reflected over. I then assigned them the task of coming up with an expression that could determine the image coordinate given the line of reflection and the pre-image point.

This entire exploration took 45 minutes, but they started to figure things out.