Orthogonal transformation

Have you ever played with toy building blocks or Legos? Sometimes, you might want to change the way the blocks look, without changing their size or shape. An orthogonal transformation is like turning and flipping the blocks in a certain way so that their position changes, but they still look the same.

In math, we use something called a coordinate system to draw pictures and graphs, kind of like a map with an x-axis and a y-axis. An orthogonal transformation is like taking that coordinate system and turning it or flipping it in a certain way, but the distances between all the points stay the same.

For example, imagine you have a square on your coordinate system. If you rotate the coordinate system by 90 degrees, the square will look different, but it will still have the same length of sides and the same angles between them. That's what an orthogonal transformation is - changing the position or orientation of something, but keeping all the basic measurements the same.