Lesson 4

Students continue to investigate the effects of transformations. The new feature of this lesson is the coordinate plane. In this lesson, students use coordinates to describe figures and their images under transformations in the coordinate plane. Reflections over the \(x\)-axis and \(y\)-axis have a very nice structure captured by coordinates. When we reflect a point like \((2,5)\) over the \(x\)-axis, the distance from the \(x\)-axis stays the same but instead of lying 5 units above the \(x\)-axis the image lies 5 units below the \(x\)-axis. That means the image of \((2,5)\) when reflected over the \(x\)-axis is \((2,\text-5)\). Similarly, when reflected over the \(y\)-axis, \((2,5)\) goes to \((\text-2,5)\), the point 2 units to the left of the \(y\)-axis. 

Using the coordinates to help understand transformations involves MP7 (discovering the patterns coordinates obey when transformations are applied).