Math 2 Unit 1 Transformations & Symmetry

reflect point n over the x axis

(-1,-4)

At what degree did this triangle rotate

270 degrees clockwise or 90 degrees counterclockwise

In a reflection, the line of reflection intersects the line segments connecting corresponding points of the pre-image at a ________

90 degree angle

reflection

Moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding preimage and image points

rotation

Moves points along concentric circles

Translation

Moves points the same distance along lines that are parallel to each other

TRUE OR FALSE: In a rotation, the line segment connecting the pre-image to center/point of rotation is the same length as the line segment connecting the image to the center/point of rotation because all radii of a circle are congruent.

TRUE

Identify the transformation.

Translation 5 units left, 1 unit up.

Which rule would result in a translation of 2 units left and 3 units up? a. (x, y) → (2x, 3y) b. (x, y) → (x + 3, y - 2) c. (x, y) → (x - 2, y + 3) d. (x, y) → (x + 2, y - 3)

c. (x, y) → (x - 2, y + 3)

Write a function rule that will transform a geometric figure by translating the figure 2 units to the right and 1 unit down, followed by a reflection over the x-axis. Rule #1-translation: Rule #2-reflection: a. (x,y) -> (x - 6, y) b. (x,y) -> (-x, y) c. (x,y) -> (x +2, -y +1) d. (x,y) -> (x, -y)

c. (x,y) -> (x +2, -y +1)

Write a function rule that will transform the image point A'(2,-1) back to its preimage point A(2,1) using a reflection. Describe the type of reflection/line of reflection. a. (x,y) -> (x - 6, y) b.(x,y) -> (x +2, -y +1) c.(x,y) -> (x, -y) d.(x,y) -> (x, -y)

c.(x,y) -> (x, -y)

Triangle A'B'C' is formed from Triangle ABC by the transformation (x,y) -> (x+2, y-3). Exactly how many pairs of corresponding sides are parallel? How do you know? What type of transformation is this? a. 0-reflection b. 1-translation c. 2-reflection d. 3-translation e. 3-rotation

d. 3-translation

Which is the vector notation for a transformation of a figure 2 units left and 3 units up? a. <-2,-3> b. <3,-2> c. <2,-3> d. <-2,3>

d. <-2,3>

In a rotation, the pre-image and image will stay ______________ from the center of rotation

equidistant

The result of a transformation is called the ___________

image

In a reflection, the line of reflection intersects the line segments connecting corresponding points of the pre-image and image. It is known as a _______ because it intersects the line segments at the midpoint of each segment and forms a 90 degree angle.

perpendicular bisector

Identify the transformation from ABC to A'B'C'. How do you know? What is the rule? What are the pre-image and image points?

reflection across the x axis

Given the line 2x-3y=9, identify the equation of a line that is perpendicular to the given line. Given equation in slope intercept form:

y = -3/2x + 5

The pre-image is graphed at (-1,-4) and the image is graphed at (3,4). Graph on graph paper and clearly draw the line of reflection and write the equation of the line.

y = 1/4x + 1/2