Transformations, congruence, vectors and similarity Study Guide

Reflection is a type of geometric transformation where a figure is flipped over a line, called the line of reflection or mirror line. The reflected image maintains the same size and shape as the original figure but is oriented in the opposite direction. Imagine folding a piece of paper along the line of reflection; the original figure and its image would perfectly overlap. Every point in the original figure is the same perpendicular distance from the line of reflection as its corresponding point in the image. For example, if point A is 2 units away from the line of reflection, its image A' will also be 2 units away from the line, on the opposite side. Common lines of reflection include the x-axis, y-axis, the line y = x, the line y = -x, and horizontal or vertical lines like y = k or x = k. To perform a reflection, you identify the line of reflection, then for each key point of the original figure, you find its image by measuring the perpendicular distance to the line of reflection and extending that same distance on the other side. Connecting these image points will form the reflected figure.

Reflection is a type of geometric transformation that creates a mirror image of a shape. When a shape is reflected, every point in the original shape is mapped to a corresponding point on the other side of a 'mirror line', also known as the line of reflection or mirror line. The distance from any point on the original shape to the mirror line is exactly the same as the distance from its reflected point to the mirror line, and this distance is always measured perpendicular to the mirror line. The orientation of the shape is reversed; if the original shape reads from left to right, its reflection will read from right to left. Crucially, the size and shape of the object remain unchanged after a reflection; it is a rigid transformation. Common mirror lines include the axes (x-axis and y-axis), and lines like y = x, y = -x, or horizontal/vertical lines such as x = 3 or y = -2. To perform a reflection, you identify the mirror line, then for each vertex of the shape, you draw a perpendicular line from the vertex to the mirror line and extend it an equal distance on the other side to find the reflected vertex. Connecting these new vertices forms the reflected image.