Translations and Vectors

13.1/13.2 Translations and Reflections

Transformations

• Think about how many different ways you can transform an object

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

Translation

• 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)

Multiple Choice

Pick which image shows the object graphed with the given translation: (x,y) -> (x+4, y+4)

Translation Vectors

• 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

Multiple Select

How would we describe this vector? Select all that may apply

• Down 2 units

• Down 1 unit

• Left 3 units

• Right 4 units

13.2 Reflections

Reflecting over an axis

• 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)

Multiple Choice

What would the point of R' be reflected over y=-2?

• (-2, -2)

• (-2, -7)

• (-2, -3)

• (2, 7)