Transformations - Rotations

We turn our papers when drawing rotation to predict where and how the rotation will turn out. This is because when you turn the paper, the original figure will be in the same position that the rotated figure will be. A rotated figure does not change in size, shape, or location. A rotated figure differs from a reflection because a reflection is when you make a figure on the opposite side of a line of symmetry. And a rotation is when you rotate a figure around a center point. If you rotate a figure 90 degrees clockwise and then 90 degrees counterclockwise, it will end up in the same position that it started. The same thing will happen if you rotate the figure 360 degrees counterclockwise, the only difference is that it will be upside down. The difference between rotating a figure clockwise or counter clock wise is that counterclockwise goes in the opposite direction.

Transformations - Reflections

A reflection is like a mirror image because in a reflection, the size nor the shape changes, only the position. You could reflect an image over the x-axis or y-axis without knowing the exact rules by using equidistant, which means that the reflected figure has to be the equal distance from the x or y-axis as the original figure. The original figure and it's reflection are exactly the same distance from the line of symmetry so that the figures will stay the same.We could determine the line of symmetry if we are given the points of the original figure and the image, all we would have to do is take the space between them and divide it in half, and that's were the line of symmetry would go. When looking at two figures, we know which one is the transformation because the transformation has an apostrophe over the top, for example, the points on the original figure would be labeld A, B, and C and the transformation would be A', B', and C'.

Transformations - Dilation's

A dilated figure does not change in shape or location, however it does change in size. It will either get larger or smaller. When we zoom into a photo, it gets bigger and that does relate to dilation because the figure can get larger. If a figure undergoes dilation with a scale factor of 1.5 the figure will get bigger, and if the scale factor is 0.5, the figure will get smaller because when the scale factor is greater than 1, the figure gets larger and when the scale factor is less than 1, the figure will get smaller. Dilation differ from translations because translation is when you slide the figure to a different location and for dilation, the figure will either get smaller or larger. Moreover in all dilation's, the origin will be the center. Multiplying 1/3 is the same as dividing by 3 because if u divide the number by three then u get the same as if you were to multiply. For example, 1/3 x 6 = 2 and 6 divided by 2 = 3.

Transformations - Translations

When looking at two figures, you know which one is the transformation because the one who is that transformation has an apostrophe sign. For example, M is the original and M' is the transformation. The new points are called prime (which is what the apostrophe stands for). Another word that you can use to describe a translation is sliding. A translated figure will never change shape because translating means to slide a figure up, down and across any number of units. You can translate a figure without using a coordinate plane by seeing on how many units you have to slide the figure. For example, if you have to translate a figure 5 units to the right and the original figure is on the points, (5,3) you will have to add 5+5 because when your sliding it to the right, you are moving it on the x-axis and the x-axis is the first number, which in this case is 5 because u started with (5,3). In other words, you can translate a figure by finding out if your going to slide it on the x-axis or the y-axis, if you going to the left u will be subtracting from the x-axis and if u go to the right, you will be adding it. And if you go up on the y-axis, you will add and if u go down, you will subtract.