Transformation Rules
What is congruency?
Same shape and size
In translations, do the vertices maintain congruence? Explain
Yes, they only slide and do not reflect.
Given A(4,5) find A` after it is reflected over the x-axis:
A`(4,-5)
We know that dilations do not maintain congruence, what word do we use to describe how the shapes are related?
Similar
If no direction is given, what direction do we assume we rotate?
Counter Clockwise
Does the coordinate grid I, II, III, IV go clockwise or counter clockwise?
Counter Clockwise
Describe the movement of a figure with the rule (x+1, y-2)
1 unit to the right and 2 units down
Given J(2,-3) find J` after a reflection over the line y=2
J`(2,7)
Will this get bigger or smaller? and why.
(x,y) —> (.2x, .2y)
Smaller, it is multiplied by a number smaller than 1
If you rotate a point (x,y) clockwise 90 degrees about the origin, what is the resulting point?
(y,-x)
What transformation(s) do not maintain a shapes congruency?
Dilations
What is the result of the following: T<1,-2>(-1,5)
(0,3)
What is the rule for reflecting a general point (x,y) over the line y=-x?
(x,y)->(-y,-x)
Given triangle J'A'N' is the result of JAN after a dilation. If JA = 8, AN = 10, J'A' = 12, what is A'N'?
A'N' = 15
Given triangle JAN has coordinates J(0,1), A(-3,5), and N(2,-4). What will N` be after a 90 degree counter clockwise rotation?
N' (4,2)
Which transformations maintain congruency?
Translations, Rotations, and Reflections
(or Rigid Motions)
What does the rule: (x, y) -> (x+3, y) represent
Translate 3 units right
Find the reflection of (4,3) over y=x
(3,4)
Given CAT and PIG are similar figures, and CA = 10 and PI = 4, what is the common ratio from CAT to PIG?
4/10 or .4
If I start with a point (x,y) in quadrant I, which two rotations would get me to quadrant IV? (Be sure to name direction and degree for each rotation)
90 clockwise and 270 counter clockwise
Which types of transformations never change the shapes orientation?
Dilations and translations
Given triangle JAN has coordinates J(0,1), A(-3,5), and N(2,-4). What will A` be after a translation by vector <5,-6>?
A`(2,-1)
If figure is in quadrant I and is reflected across the y axis, and then reflected over the line y=x, what quadrant will it be in?
quadrant IV
A figure is going to be dilated by a scale factor of k. If the original area of the shape is A, what will be the area of the dilated figure?
A*k^2
Given A(4,-3), what is A' after a rotation of 90 degrees around the point (1,-2)?
(2,1)