Test:
Transformation Geometry II - Challenging
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Question 1:
Find the triangle
A
B
C
under a reflection across the line
y
=
−
x
, where
A
(
3
,
−
1
)
,
B
(
−
1
,
3
)
,
C
(
2
,
4
)
:
A
A
′
=
(
1
,
−
3
)
,
B
′
=
(
−
3
,
1
)
,
C
′
=
(
−
4
,
−
2
)
B
A
′
=
(
−
3
,
1
)
,
B
′
=
(
1
,
3
)
,
C
′
=
(
4
,
2
)
C
A
′
=
(
−
3
,
−
1
)
,
B
′
=
(
3
,
1
)
,
C
′
=
(
2
,
−
4
)
D
A
′
=
(
3
,
1
)
,
B
′
=
(
−
3
,
−
1
)
,
C
′
=
(
−
2
,
4
)
Question 2:
Find the triangle
A
B
C
under a reflection across the line
y
=
−
x
, where
A
(
−
5
,
2
)
,
B
(
−
1
,
3
)
,
C
(
1
,
−
3
)
:
A
A
′
=
(
−
2
,
5
)
,
B
′
=
(
−
3
,
1
)
,
C
′
=
(
3
,
−
1
)
B
A
′
=
(
−
5
,
−
2
)
,
B
′
=
(
3
,
−
1
)
,
C
′
=
(
−
3
,
−
1
)
C
A
′
=
(
2
,
5
)
,
B
′
=
(
−
1
,
−
3
)
,
C
′
=
(
1
,
3
)
D
A
′
=
(
5
,
−
2
)
,
B
′
=
(
1
,
−
3
)
,
C
′
=
(
1
,
3
)
Question 3:
Find the coordinates of the triangle
A
B
C
enlarged by a factor of
2
:
A
A
′
=
(
2
,
−
4
)
,
B
′
=
(
−
4
,
4
)
,
C
′
=
(
4
,
2
)
B
A
′
=
(
4
,
−
2
)
,
B
′
=
(
4
,
−
4
)
,
C
′
=
(
2
,
4
)
C
A
′
=
(
−
4
,
−
2
)
,
B
′
=
(
−
4
,
−
4
)
,
C
′
=
(
−
2
,
4
)
D
A
′
=
(
−
4
,
2
)
,
B
′
=
(
4
,
4
)
,
C
′
=
(
2
,
−
4
)
Question 4:
Find the coordinates of the triangle
A
B
C
enlarged by a factor
−
1
2
and centered about the origin:
A
A
′
=
(
−
1
,
4
)
,
B
′
=
(
−
2
,
2
)
,
C
′
=
(
−
1
,
1
)
B
A
′
=
(
−
4
,
1
)
,
B
′
=
(
1
,
−
1
)
,
C
′
=
(
−
1
,
1
)
C
A
′
=
(
−
16
,
4
)
,
B
′
=
(
−
8
,
8
)
,
C
′
=
(
−
4
,
4
)
D
A
′
=
(
4
,
−
1
)
,
B
′
=
(
2
,
−
2
)
,
C
′
=
(
1
,
−
1
)
Question 5:
Find the coordinates of the triangle
A
B
C
rotated by
90
°
about the origin:
A
A
′
=
(
1
,
2
)
,
B
′
=
(
1
,
0
)
,
C
′
=
(
4
,
1
)
B
A
′
=
(
1
,
3
)
,
B
′
=
(
1
,
1
)
,
C
′
=
(
4
,
2
)
C
A
′
=
(
1
,
0
)
,
B
′
=
(
3
,
0
)
,
C
′
=
(
2
,
3
)
D
A
′
=
(
1
,
1
)
,
B
′
=
(
3
,
1
)
,
C
′
=
(
2
,
4
)
Question 6:
Find the coordinates of the triangle
A
B
C
rotated by
180
°
about the origin:
A
A
′
=
(
1
,
−
3
)
,
B
′
=
(
−
1
,
−
7
)
,
C
′
=
(
−
2
,
−
4
)
B
A
′
=
(
−
3
,
−
1
)
,
B
′
=
(
−
7
,
1
)
,
C
′
=
(
−
4
,
2
)
C
A
′
=
(
−
1
,
3
)
,
B
′
=
(
1
,
7
)
,
C
′
=
(
2
,
4
)
D
A
′
=
(
−
3
,
1
)
,
B
′
=
(
−
7
,
−
1
)
,
C
′
=
(
−
4
,
−
2
)
Question 7:
Find the coordinates of the triangle
A
B
C
rotated by
270
°
about the origin:
A
A
′
=
(
1
,
−
1
)
,
B
′
=
(
0
,
3
)
,
C
′
=
(
−
2
,
−
4
)
B
A
′
=
(
1
,
−
1
)
,
B
′
=
(
3
,
0
)
,
C
′
=
(
2
,
−
4
)
C
A
′
=
(
−
1
,
1
)
,
B
′
=
(
−
3
,
0
)
,
C
′
=
(
−
2
,
4
)
D
A
′
=
(
1
,
1
)
,
B
′
=
(
3
,
0
)
,
C
′
=
(
2
,
4
)
Question 8:
Find the coordinates of the triangle
A
B
C
rotated by
−
90
°
about the origin:
A
A
′
=
(
0
,
2
)
,
B
′
=
(
1
,
4
)
,
C
′
=
(
−
1
,
5
)
B
A
′
=
(
0
,
−
2
)
,
B
′
=
(
1
,
−
4
)
,
C
′
=
(
−
1
,
−
5
)
C
A
′
=
(
2
,
0
)
,
B
′
=
(
4
,
1
)
,
C
′
=
(
5
,
−
1
)
D
A
′
=
(
−
2
,
0
)
,
B
′
=
(
−
4
,
−
1
)
,
C
′
=
(
−
5
,
1
)
Question 9:
Find the coordinates of the triangle rotated by
90
°
about the origin and enlarged by a factor of
2
:
A
A
′
=
(
−
1
,
1
)
,
B
′
=
(
−
8
,
4
)
,
C
′
=
(
−
4
,
8
)
B
A
′
=
(
2
,
−
2
)
,
B
′
=
(
4
,
−
2
)
,
C
′
=
(
2
,
−
4
)
C
A
′
=
(
2
,
2
)
,
B
′
=
(
8
,
4
)
,
C
′
=
(
4
,
8
)
D
A
′
=
(
2
,
2
)
,
B
′
=
(
8
,
2
)
,
C
′
=
(
2
,
4
)
Question 10:
Find the coordinates of the triangle
A
B
C
rotated by
180
°
about the origin and enlarged by a factor of
−
1
3
:
A
A
′
=
(
−
1
,
−
2
)
,
B
′
=
(
2
,
2
)
,
C
′
=
(
3
,
−
2
)
B
A
′
=
(
−
1
,
2
)
,
B
′
=
(
−
2
,
1
)
,
C
′
=
(
−
3
,
3
)
C
A
′
=
(
2
,
1
)
,
B
′
=
(
1
,
2
)
,
C
′
=
(
3
,
3
)
D
A
′
=
(
1
,
2
)
,
B
′
=
(
2
,
1
)
,
C
′
=
(
3
,
3
)
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