(1) How to construct a REFLECTION
b) Placing your compass pointer at A, extend the compass to
reach past the line of reflection so that when you make an arc
you create two intersections (in our case at D and E).
a) Given AB and a line of reflection.
B
B
D
A
A
E
c) Leaving your compass with the same measurement that you
just used to create D and E, place your pointer at D and create
an arc on the opposite side of A.
d) Do the same thing but from E. Place your pointers at E and
with that same measurement create an arc that intersects the
arc that you just made from D. The intersection of these two
arcs is A’
B
B
D
D
A
A
E
A'
E
e) Repeat the steps b-d but from B. Placing your compass at B,
extend your compass so that it reaches beyond the line of
reflection. This will create two intersections (H and G in our
case).
f) Now from H create an arc of the congruent length on the
opposite side of B.
H
H
B
B
G
A
G
A
A'
g) Placing your compass at G, using the same length construct
the arc that will intersect with the arc you just made.
A'
h) The intersection is B’. Draw A ' B ' .
H
H
B
B
B'
B'
G
A
G
A'
A
A'
(2) How to construct a ROTATION
b) Placing the pointer of your compass on O, create the
arcs through B and through A in a positive direction
(counter-clockwise). We know that A and B will move on
these arcs during the rotation.
a) Rotate AB about point O, 100°.
A
A
B
B
O
O
c) Create OB , this will act as one side of the 100° angle
that we are going to create.
d) Place your protractor along OB , with the center of the
protractor at O. Measure 100° from OB . Create a
reference mark for 100°.
A
A
B
B
O
O
e) Create the ray through the mark that you created.
Where that ray intersects the arc that B is on, is B’
f) Create OA , then position your protractor to measure
100. Make a mark at 100.
A
A
B'
B'
B
O
100°
B
O
g) Create the ray through the mark that you created.
Where the ray intersects the arc that A is on, is A’.
h) Draw in A ' B '
A
A'
B'
A
A'
B'
B
O
B
O
(3) How to construct a TRANSLATION
a) Given a ABC and vector AA ' .
b) In a translation all points move by vector AA ' (the
same direction and the same distance) so we use our
compass to measure the distance AA’. Use that
measurement to make an arc from B and from C. We
know that B and C must move that far in that general
direction.
B
B
C
C
A
A
A'
A'
c) Next we want to find the exact location of B’ on the arc
that we just created. To do this we measure AB using our
compass and then from A’ we create that arc until it
intersect with the arc drawn from B. The intersection of
these two arcs forms B’.
d) We do the same to find C’ but we measure AC using our
compass and then create the arc from A’ until it intersects
the arc we made from C. This intersection is C’
B
B
C
C
B'
B'
A
A
A'
A'
e) Connect A’B’, B’C’ and C’A’ to complete the triangle.
B
C
B'
A
C'
A'
C'
(4) How to construct the Line of Reflection
Connect any vertex of ΔDEF to its image (E to E'). Construct the perpendicular bisector of the segment formed.
It is sufficient to choose only one set of corresponding points to get
the line of reflection. You need not bisect all three connected segments, unless you want to test the accuracy of your
construction.
(5) How to construct the Point of Rotation
Connect any vertex of the preimage to its image. Construct the perpendicular bisector of the segment formed. Repeat
this for another vertex of the preimage and image. The point of intersection is the point of rotation.