1. 2D - GEOMETRY POSITIONS ON THE GRID TRANSLATIONS REFLECTIONS ROTATIONS
CONGRUENCE & SIMILARITY

2. POSITIONS ON A GRID Cartesian Coordinate System Axis intercept at “0”
X – axis runs horizontally
Y – axis runs vertically
We read the information as
an ordered pair ( X , Y )
Ex. – ( 3 , 4 ) ●
POSITIONS ON A GRID

3. POSITIONS ON A GRID See if you can plot these points on the graph
( 3 , 4 )
( -2 , 6 )
( 5 , -1 )
POSITIONS ON A GRID

4. TRANSLATIONS Ex. Triangle ABC Point A ( 6 , 7 ) Point B ( 7, 3 )
Translation is a term used in
geometry to describe a function that
moves an object a certain distance.
The object is not altered in any other
way. It is not rotated, reflected or
re-sized. In a translation, every
point of the object must be moved
in the same direction and for the
same distance.
Ex. Triangle ABC
Point A ( 6 , 7 )
Point B ( 7, 3 )
Point C ( 2 , 4 ) A C B
TRANSLATIONS

5. TRANSLATIONS Triangle ABC moves 2 down and 3 back OR y = -2 and x = -3
RISE over RUN
a = −2 − 3
It’s new position is (3,5), (4,1), (-1,2) A A C B C B
TRANSLATIONS

6. REFLECTIONS A transformation in A B which a geometric figure
is reflected across a line, C D
creating a mirror image.
That line is called the
axis of reflection.
REFLECTIONS

7. REFLECTIONS In order to show reflection, we must use
the line of axis as our
reference line and count
our RISE over our RUN
and REVERSE it like a
mirror.
What did you do to get
to the line of reflection? A B C D D C B A
From point B – to get to (0,0) you have to go
6 down (y = -6) and back 7 (x = -7)
From point D – to get to (0,0) you have to go
1 down (y = -1) and back 7 (x = -7)
From point C – to get to (0,0) you have to go
1 down (y = -1) and back 2 (x= -2)
From point A – to get to (0,0) you have to go
6 down (y = -6) and back 2 (x = -2)
REFLECTIONS

8. ROTATIONS A fixed point around which other points rotate
in either a (CW) clock-wise
or counter clockwise (CCW)
direction A B
The center of the rotation C D
may be inside or outside
the object or shape
Center of rotation point = (0,0)
ROTATIONS

9. ROTATIONS Rotation from Center of rotation point (0,0)D B
Rotation from Center of
rotation point (0,0)
90̊ (CW) – clockwise
90˚ (CCW) – counter
clock wise C A C A A B D C B D
Center of rotation point = (0,0)
ROTATIONS

10. CONGRUENCY & SIMILARITY
Congruency = the same
Can be rotated, reflected,
or translated
Similarity = Proportional
(meaning – smaller or
bigger)
Can also be rotated,
reflected, or translated
x 2
CONGRUENCY & SIMILARITY

11. CONGRUENCY & SIMILARITY
(the same)
Translation - −7 −4
Reflection – Line = y = - 1
Rotation – CW 180º A A B B C C A B C C B A
CONGRUENCY & SIMILARITY

12. CONGRUENCY & SIMILARITY
(proportional: bigger or
smaller)
We can also translate,
rotate, or reflect
CONGRUENCY & SIMILARITY