Dilations
Translations
Slope
Reflections or Rotations
Sequence of Transformations
100
A dilation is when a shape....
gets proportionally bigger or smaller
100
A translation of a shape is when...
All points of a shape move the same distance and direction.
100
Slope is Calculated by...
Rise/Run
100
A reflection over the x-axis would change (x,y) to become...
(x, -y)
100
What happens to a triangle when it is first dilated by a factor of 2 and then translated 4 units down?
What is 'The triangle doubles in size and then shifts 4 units down
200
Scale factor is...
how much bigger or smaller a shape gets, new/old
200
In a translation, what happens to the size and shape of a figure?
They remain the same!
200
The steepness of a line depends on the slope, when the slope of the line becomes a greater value what happens to the steepness?
It becomes steeper, and as the slope approaches 0 the line will flatten out.
200
Triangle PQR is rotated 90 degrees counter clockwise about the origin to form the image triangle P'Q'R' (not shown). What are the signs of the coordinates (x,y) of point P'?
A. Both x and y are positive
B. x is negative and y is positive
C. Both x and y are negative
D. x is positive and y is negative
D. x is positive and y is negative
DAILY DOUBLE BONUS QUESTION:
What are the coordinate points for point P'?
200
A rectangle is graphed on a coordinate plane. Which transformation will result in a rectangle that is NOT congruent to the original rectangle?
A. A Translation 4 units up and a reflection across the x-axis
B. A rotation of 180 degrees counterclockwise
C. A dilation by a scale factor of 3
D. A reflection across the x-axis
C dilation by a scale factor of 3 would mean the shape is similar but NOT congruent.
300
How would you write the rule (ie. how do the x and y change?) for a shape that was reduced by a third?
(x,y)-->(1/3x, 1/3y)
300
If the point (-3,5) is translated 4 units to the right and 2 units down, what are the new coordinates?
(1,3)
300
What type of slope does a line have if it moves upward from left to right?
A positive slope
300
What happens to a shape when it is reflected across the y-axis?
It creates a mirror image
300
Seven line segments are shown. Which of these could be the image of segment AB after a sequence of reflections, rotations, and/or translations? There is more than one answer; students must have all correct answers.
CD, GH, and NP
400
Triangle ABC is dilated by 1/4. If point B is (0,-4) where is B'?
(0,-1)
400
A circle is graphed on a coordinate grid with its center at (-4,7). The circle will be translated 6 units to the right and 9 units down.
(2, -2)
400
In what scenario can you not just count the boxes to find rise / run of a line on a graph. Explain.
When the graph doesn't count 1 box for 1 unit. For example the x and y axis is counting by 2 units.
400
Describe the rule for rotating a point 180° around the origin.
(x,y)→(−x,−y)
400
Describe the sequence of transformations that takes the point (2,3) to (4,−3), if the first transformation is a dilation by a factor of 2.
First, dilate by a factor of 2 to get (4,6), then reflect over the x-axis to get (4,−6), and finally translate 3 units up to (4,−3),
Other solves are possible
500
If rectangle LMNO is dilated from L(21,7) to L'(3,1) what was the scale factor?
The scale factor was 1/7
500
Describe the rule for translating a point by 2 units left and 3 units up.
What is (x,y)→(x−2,y+3)
500
Given the points (3,2) and (7,50), what is the slope of the line passing through these points?
Slope of 12 (48 Rise / 4 Run)
500
If the point (5,−2) is reflected across the y-axis, what are the new coordinates?
(-5,-2)
500
Describe the transformations taking place from 1 to 2 and 2 to 3
1-2: a reflection across the x-axis then a translation of (x+3,y)
2-3:
Option 1 - CCW 90 degrees, translate down 3
Option 2 - CW 270 degrees, translate down 3