My nephew is preparing for a $4$-th grade state test. They need to learn topics like reflection about $x$ or $y$-axis of a point( say $(3,5)$ reflected about the $y$-axis).
I tried to explain but he's not getting it. He's smart, but very distracted. How can I explain in an intuitive way?
On
I would say something like "Starting at the origin, $(3,5)$ means go $3$ units to the right (the $x$ direction), and then $5$ units up (in the $y$ direction). If you reflect about the $y$-axis, you have to go $3$ units to the left and then $5$ up, i.e. you're at the point $(-3,5)$.
Hopefully that helps. When I was learning it helped me to think of the Cartesian plane as a map I had to naviagate
Use the 'Battleship game' (or other) and put (virtual) boats in the four quarters to get his attention. Because the pleasure of sinking is great! :-)
Introduce horizontal and vertical mirrors if needed (and/or negative coordinates) explaining that the boats are seen or not in mirrors.