Referencing the example in step 3, we would shift the reflected object 2 units to the left after reflecting it. Undo the translation that mapped the horizontal or vertical line to the corresponding axis.Perform the reflection as we would in the x-axis or y-axis reflection examples above.For example, given the vertical line y = -2, translating the line (as well as the object) 2 units to the right would map the line to the y-axis.

Translate the line and object such that a horizontal line is mapped to the x-axis, or a vertical line is mapped to the y-axis.

Consider the line of reflection and object being reflected to be a single object.

To reflect objects over horizontal or vertical lines that are not the x- or y-axes, the following steps can be used: Reflection over a horizontal or vertical line All of the points on triangle ABC undergo the same change to form DEF. Triangle ABC is reflected across the line y = x to form triangle DEF. Reflection over y = xĪ reflection across the line y = x switches the x and y-coordinates of all the points in a figure such that (x, y) becomes (y, x). Triangle DEF is formed by reflecting ABC across the y-axis and has vertices D (4, -6), E (6, -2) and F (2, -4). Algebraically, the ordered pair (x, y) becomes (-x, y). In a reflection about the y-axis, the y-coordinates stay the same while the x-coordinates take on their opposite sign.

Triangle DEF is formed by reflecting ABC across the x-axis and has vertices D (-6, -2), E (-4, -6) and F (-2, -4). Algebraically, the ordered pair (x, y) becomes (x, -y). In a reflection about the x-axis, the x-coordinates stay the same while the y-coordinates take on their opposite signs. The most common cases use the x-axis, y-axis, and the line y = x as the line of reflection. There are a number of different types of reflections in the coordinate plane. This is true for any corresponding points on the two triangles and this same concept applies to all 2D shapes. A, B, and C are the same distance from the line of reflection as their corresponding points, D, E, and F. The figure below shows the reflection of triangle ABC across the line of reflection (vertical line shown in blue) to form triangle DEF. The same is true for a 3D object across a plane of refection. In a reflection of a 2D object, each point on the preimage moves the same distance across the line of reflection to form a mirror image of itself. The term 'preimage' is used to describe a geometric figure before it has been transformed 'image' is used to describe it after it has been transformed. When an object is reflected across a line (or plane) of reflection, the size and shape of the object does not change, only its configuration the objects are therefore congruent before and after the transformation. In geometry, a reflection is a rigid transformation in which an object is mirrored across a line or plane. Find a point on the line of reflection that creates a minimum distance.Home / geometry / transformation / reflection ReflectionĪ reflection is a type of geometric transformation in which a shape is flipped over a line.Determine the number of lines of symmetry.Describe the reflection by finding the line of reflection.Where should you park the car minimize the distance you both will have to walk? You need to go to the grocery store and your friend needs to go to the flower shop. Now we all know that the shortest distance between any two points is a straight line, but what would happen if you need to go to two different places?įor example, imagine you and your friend are traveling together in a car. And did you know that reflections are used to help us find minimum distances?

Line of reflection