Transformations Flashcards
pre-image
the original point
image
the new point
Translation (T)
move left, right, up, down
circle equation
(x-h)² + (y-k)² = r²
line of reflection, “mirror”
the line a shape is reflected across to create its mirror image; perpendicular bisector of the segment connecting the pre-image and image points
Reflection (r)
flips a shape across a line
reflection of x=y
switch x and y values
reflection over x-axis
(x, y) -> (x, -y)
reflection over y-axis
(x,y) -> (-x, y)
isometry (rigid motion)
transformation that preserves congruence (angle measure, segment length, and orientation)
quadrant I
(+, +)
quadrant II
(-, +)
quadrant III
(-, -)
quadrant IIII
(+, -)
reflection of y=-x
(x, y) -> (-y, -x)
positive rotation
counterclockwise rotation
negative rotation
clockwise rotation
all full rotations (360, -360, 720, -720)
end up in the same spot (same point/equal)
R90° and R-270°
equal, (x, y)—>(-y, x)
R180° and R-180°
equal, (x, y)—>(-x, -y)
°
combustion symbol (not multiplication) (do right to left)
degrees needed to rotate a shape to have symmetry (rotational symmetry - put point in center and draw a line from the center point to each point of the shape)
360/n
which transformation is an opposite/indirect isometry? (orientation not preserved)
reflection
which transformations are direct isometries? (orientation preserved)
rotations and translations
dilation equation
(x,y) –> (kx, ky)
k (scale factor)
the ratio in relation to the center of dilation (makes figure bigger or smaller)
if the scale factor is greater than 1
the figure becomes larger
if the scale factor is between 0 and 1
the figure becomes smaller
scale factors that produce a congruent figure
k=1, k=-1
image divided by pre-image
equals the scale factor/k
to find pre-image after dilation
divide by the image by the scale factor
transformation
a way of changing the size or position of a shape
R270° and R-90°
equal, (x, y)—>(y, -x)
x² Graph
x^3 Graph
√x Graph
|x| Graph
