Translations and Vectors

Think about how many different ways you can transform an object

You can translate (slide), reflect, rotate, and dilation (grow or decrease in size)

Let's translate this triangle. If we wanted to translate this object 4 units to the right, and 3 units up, what would each new coordinate be?

(-1,2), (-4,5), (1,7)

Similarly to what we just did on the previous slides, we are going to be sliding an object using a vector.

The image is the square, and the vector is vector w, on the right. How would you describe the movement of this vector?

Look at where it's starting from, and where it ends (tip of the arrow)

Start at the beginning, go down 7 units, and 3 units to the left. THIS IS NOW OUR TRANSLATION DIRECTIONS

This point R is at (4,4). But what if we wanted to reflect it over the x or y axis?

What would the coordinate be of R' if we reflected it over the x axis?

(4, -4); Notice it stays at the same x coordinate, but our y coordinate will go from being at a positive 4, to reflecting and being 4 below

What about reflecting over the y axis?

(-4, 4)