When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Explanation: the line y=1 is a horizontal line passing through all. points with a y-coordinate of 1. the point (3,10) reflected in this line. the x-coordinate remains in the same position.

Reflection on a Coordinate Plane

• Reflection Over X Axis. When reflecting over (across) the x-axis, we keep x the same, but make y negative.
• Reflection Over Y Axis. When reflecting over (across) the y-axis, we keep y the same, but make x-negative.
• Reflection Across Y=X.
• Reflection Across Y=-X.

A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is (x,y)→(x,−y) .

To find the reflection of the y intercept, duplicate the y value of the point and find the x distance to the AOS then travel the same distance on the other side of the AOS. In this case, the y value of the reflection of the y intercept, (0, -1) is –1, so the reflected point will also have a y value of –1.

The function translation / transformation rules:

• f (x) + b shifts the function b units upward.
• f (x) – b shifts the function b units downward.
• f (x + b) shifts the function b units to the left.
• f (x – b) shifts the function b units to the right.
• –f (x) reflects the function in the x-axis (that is, upside-down).

A transformation takes a basic function and changes it slightly with predetermined methods. This change will cause the graph of the function to move, shift, or stretch, depending on the type of transformation. The four main types of transformations are translations, reflections, rotations, and scaling.

Example: the function g(x) = 1/x

1. Move 2 spaces up:h(x) = 1/x + 2.
2. Move 3 spaces down:h(x) = 1/x − 3.
3. Move 4 spaces right:h(x) = 1/(x−4) graph.
4. Move 5 spaces left:h(x) = 1/(x+5)
5. Stretch it by 2 in the y-direction:h(x) = 2/x.
6. Compress it by 3 in the x-direction:h(x) = 1/(3x)
7. Flip it upside down:h(x) = −1/x.

A reflection is a type of transformation. It ‘maps’ one shape onto another. When a shape is reflected a mirror image is created. If the shape and size remain unchanged, the two images are congruent.

Apply the transformations in this order:

1. Start with parentheses (look for possible horizontal shift) (This could be a vertical shift if the power of x is not 1.)
2. Deal with multiplication (stretch or compression)
3. Deal with negation (reflection)
4. Deal with addition/subtraction (vertical shift)

The following figures show the four types of transformations: Translation, Reflection, Rotation, and Dilation.

One real world example of transformations is with planes. A plane at Takeoff is the same size and shape of the same plane while landing or on the runway. It is just a Translation since the plane is just in a different angle.

Transformations. Transformation means to change. Hence, a geometric transformation would mean to make some changes in any given geometric shape.

noun, plural: transformations. (1) The act, state or process of changing, such as in form or structure; the conversion from one form to another. (2) (biology) Any change in an organism that alters its general character and mode of life; post-natal biological transformation or metamorphosis.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system. Mathematical transformations describe how two-dimensional figures move around a plane or coordinate system. A preimage or inverse image is the two-dimensional shape before any transformation.

Transformation of cells is a widely used and versatile tool in genetic engineering and is of critical importance in the development of molecular biology. The purpose of this technique is to introduce a foreign plasmid into bacteria, the bacteria then amplifies the plasmid, making large quantities of it.

Transformation enables the expression of multiple copies of DNA resulting in large amounts of protein or enzyme that are not normally expressed by bacteria. Genetic material of transformed bacteria may be used to transfect eukaryotic cells for DNA or protein expression studies.

Oswald Avery, Colin MacLeod, and Maclyn McCarty showed that DNA (not proteins) can transform the properties of cells, clarifying the chemical nature of genes. Avery, MacLeod and McCarty identified DNA as the “transforming principle” while studying Streptococcus pneumoniae, bacteria that can cause pneumonia.