EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
1.
Point J (p, q) is a vertex of
quadrilateral JKLM. What are the
coordinates of J ′ after JKLM is
rotated 180° about the origin?
+P′Q′R′ is the image produced after
reflecting +PQR across the y-axis.
If vertex P has coordinates (s, t),
what are the coordinates of P′?
A
( — p, —q )
A
(t, s)
B
(
B
(s, − t)
(− s, − t)
C
( p, q )
C
D
(− s, t)
D
2.
3.
—
p, q )
—
( q, — p)
+GHI will be dilated by a scale
factor of 3, resulting in +G′ H ′ I ′.
What rule describes this
transformation?
(
)
A
(x′, y′) = 1 x, 1 y
B
(x′, y′) = (3x, 3 y)
C
(x′, y′) = (x + 3, y + 3)
D
(x′, y′) = (x − 3, y − 3)
Page 1
3
3
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
4.
What is the rule for the
transformation formed by a
translation 2 units to the left and
3 units up followed by a 90°
counterclockwise rotation?
5.
The point G ( 2, —7 ) is transformed
according to the rule
( x′, y′ )
= ( x + 2, y − 3 ) . The image G′
of the transformation is then
A
( x′′, y′′ ) = ( —3 y, —2x )
B
( x′′, y′′ ) = ( x − 2, y + 3 )
of G′′ ?
C
( x′′, y′′) =
⎡⎣ − ( y + 3 ) , x − 2⎤⎦
A
( 4, 10 )
D
( x′′, y′′) =
⎡⎣ − ( y − 2 ) , x + 3⎤⎦
B
( 4, —10 )
C
( —10, 4 )
D
( —4, 10 )
Page 2
reflected over the line y = x, resulting
in point G′′ . What are the coordinates
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
+G′H′I′ is the image of +GHI after a transformation.
6.
y
+6
G
H
+5
+4
+3
+2
+1
—6 —5 —4 — 3 —2 —1 0
—1
—2
I
+1 +2 +3 +4 +5 +6
x
G′
H′
—3
—4
—5
—6
I′
Which choice describes the transformation shown?
A
reflection over x-axis
B
reflection over y-axis
C
( x′, y′ ) = ( x − 8, y )
D
( x′, y′ ) = ( x,
Page 3
y − 8)
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
7.
Point J ( p, q ) is a vertex of
+JKL.
What are the coordinates of J ′
after JKL is reflected across the
+
line y = x ?
A
( — p, — q )
B
(
p, — q
)
C
( q, — p)
D
( q, p)
Page 4
8.
+XYZ is dilated by a factor of 12 .
What is the ratio of the area of + XYZ
to the area of its image, + X ′ Y ′ Z′ ?
A
4:1
B
2:1
C
1:2
D
1:4
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
9.
+DEF is reflected across the line y = x.
y
+6
+5
+4
E
+3
+2
+1
—6 — 5 — 4 — 3 —2 —1 0
—1
D
+1 +2 +3 +4 +5 +6
F
x
—2
—3
—4
—5
—6
Which matrix multiplication shows how to find
A
⎡1 0 ⎤ ⎡4 5 6 ⎤
⎢⎣0 1⎥⎦ ⎢⎣ 1 3 1⎥⎦
B
⎡0 1 ⎤ ⎡ 4 5 6 ⎤
⎢⎣1 0 ⎥⎦ ⎢⎣ 1 3 1⎥⎦
C
⎡ —1
⎢
⎣ 0
D
Page 5
⎡ 0
⎢—
⎣ 1
—
—
+D′E′F′ ?
0⎤ ⎡ 4 5 6 ⎤
⎥⎢
⎥
1⎦ ⎣ 1 3 1 ⎦
1⎤ ⎡ 4 5 6 ⎤
⎥⎢
⎥
0⎦ ⎣ 1 3 1 ⎦
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
10.
Triangle MRT has vertices at M ( 3, 8 ), R( 7, — 2 ), and T ( —5, — 4 ). If the triangle is to be
translated by the rule ( x′, y′) = ( x + 3, y − 2 ), which matrix expression models the
translation?
A
B
C
D
Page 6
⎡3
⎢8
⎣
7
—
2
⎡3
⎢8
⎣
7
—
2
⎡3
⎢8
⎣
7
—
2
⎡3
⎢8
⎣
7
—
2
5⎤ ⎡ 3
+ —
4 ⎥⎦ ⎢⎣ 2
—
—
3⎤
2⎥⎦
2
3
—
2⎤
3⎥⎦
5⎤ ⎡ —2
+
4 ⎥⎦ ⎢⎣ 3
—
2
3
—
2⎤
3⎥⎦
5⎤ ⎡ 3
− —
4 ⎥⎦ ⎢⎣ 2
—
—
—
—
—
—
3
2
5⎤ ⎡ —2
−
4 ⎥⎦ ⎢⎣ 3
—
—
—
—
3
2
—
3⎤
2⎥⎦
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
North Carolina Testing Program
EOC Mathematics Geometry Sample Items Goal 3
11.
+STU to +S′T ′U′ ?
Which matrix calculation was used to transform
y
+ 10
+9
U
+8
+7
+6
+5
+4
+3
T
S
+2
+1
— 10 — 9 — 8 — 7 — 6 — 5 — 4 — 3 — 2 — 1 0
—1
—2
S′
+ 1 +2 + 3 +4 + 5 + 6 +7 + 8 +9 +10
x
T′
—3
—4
—5
—6
—7
—8
—9
U′
— 10
A
⎡0
⎢1
⎣
B
⎡ —1
⎢ 0
⎣
C
⎡ —1 0 ⎤ ⎡ — 7
⎢ 0 1⎥ ⎢ 0
⎣
⎦⎣
D
⎡ 0
⎢ —1
⎣
Page 7
1⎤ ⎡ — 7
0 ⎥⎦ ⎢⎣ 0
—
—
0⎤ ⎡ — 7
— ⎥⎢
1⎦ ⎣ 0
1 ⎤ ⎡ —7
0 ⎥⎦ ⎢⎣ 0
—
4
2
—
—
4
2
3⎤
8 ⎥⎦
—
4
2
4
2
—
—
—
3⎤
8 ⎥⎦
3⎤
8 ⎥⎦
—
3⎤
8 ⎥⎦
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
12.
13.
+GHJ with vertex matrix ⎡⎢⎣ 42
3 3⎤
1
— ⎥ is dilated by a factor of 3 . In the image
6 2⎦
what are the coordinates of the vertex that lies in the second quadrant?
—
A
(
B
(
C
(1, )
D
(1, 2)
−7
, 13
3
3
−2
, 4
3
3
+G′H′J′,
)
)
—2
3
The vertices of quadrilateral GHIJ are G( —1, —1 ), H ( 3, — 2 ), I ( 2, 4 ), and J ( — 2, 3 ).
G′H ′I ′J′ is the image produced by translating quadrilateral GHIJ 6 units to the left.
Which matrix represents G′H ′I ′J′ ?
A
⎡ —7
⎢—
⎣ 7
B
⎡ —7
⎢—
⎣ 1
C
⎡ —1
⎢—
⎣ 7
D
Page 8
⎡ 5
⎢ —1
⎣
8⎤
— ⎥
3⎦
—
3
—
8
—
4
—
2
—
—
3
—
2
—
4
4
—
8⎤
⎥
3⎦
3
—
8
2
—
2
—
2⎤
⎥
3⎦
—
—
9 8 4⎤
2 4 3⎥⎦
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
14.
+M′ N′O′ is the image of +MNO produced by a translation 3 units left and 1 unit up.
⎡ —1 2 4 ⎤
. Which is the vertex matrix for +MNO ?
The vertex matrix for +M′ N′O′ is ⎢
1 6 —3 ⎥
⎣
A
B
⎡2 5
⎢0 5
⎣
⎡ —4
⎢ 2
⎣
—
7⎤
4 ⎥⎦
1
7
—
—
C
⎡ — 2 1 3⎤
⎢ 4 9 0⎥
⎣
⎦
D
⎡ 0 3
⎢ —2 3
⎣
Page 9
—
⎦
1⎤
2⎥⎦
5⎤
6 ⎥⎦
Published December 2007. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOC Mathematics Geometry Sample Items Goal 3
North Carolina Testing Program
15.
Polygon FGHI is represented by vertex matrix M.
⎡ 2
M = ⎢—
⎣ 2
—
4
2
4
5
—
—
2⎤
5⎥⎦
Which multiplication would be used to reflect polygon FGHI across the x-axis?
A
B
C
D
⎡1
⎢0
⎣
0⎤ ⎡ 2
1 ⎥⎦ ⎢⎣ — 2
—
⎡ —1 0 ⎤ ⎡ 2
⎢ 0 1⎥ ⎢ —2
⎣
⎦⎣
⎡ —1
⎢ 0
⎣
⎡ 0
⎢ —1
⎣
0⎤ ⎡ 2
1⎥⎦ ⎢⎣ — 2
—
1⎤ ⎡ 2
0 ⎥⎦ ⎢⎣ — 2
—
4
2
—
4
5
—
—
4
2
—
4
5
—
—
4
2
—
—
4
2
—
—
2⎤
5 ⎥⎦
2⎤
5 ⎥⎦
4
5
—
4
5
—
2⎤
5⎥⎦
2⎤
5⎥⎦
End of Goal 3 Sample Items
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Page 10
Published December 2007. May reproduce for instructional and
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EOC
Geometry Goal 3
Sample Items Key Report
1
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Applying
A
Thinking Skill:
Correct Answer:
2
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Applying
B
Thinking Skill:
Correct Answer:
3
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Applying
D
Thinking Skill:
Correct Answer:
4
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Analyzing
C
Thinking Skill:
Correct Answer:
5
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Analyzing
C
Thinking Skill:
Correct Answer:
6
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Analyzing
D
Thinking Skill:
Correct Answer:
7
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Applying
D
Thinking Skill:
Correct Answer:
8
Objective:
3.01
Describe the transformation (translation, reflection, rotation, dilation) of polygons in
the coordinate plane in simple algebraic terms.
Analyzing
A
Thinking Skill:
Correct Answer:
Page 1
Published December 2007. May reproduce for instructional and educational
purposes only; not for personal or financial gain.
EOC
Geometry Goal 3
Sample Items Key Report
9
Objective:
3.02
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
Analyzing
B
Thinking Skill:
Correct Answer:
10
Objective:
3.02
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
Applying
A
Thinking Skill:
Correct Answer:
11
Objective:
3.02
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
Applying
B
Thinking Skill:
Correct Answer:
12
Objective:
3.02
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
Analyzing
B
Thinking Skill:
Correct Answer:
13
Objective:
3.02
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
Applying
B
Thinking Skill:
Correct Answer:
14
Objective:
3.02
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
Applying
A
Thinking Skill:
Correct Answer:
15
Objective:
3.02
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
Applying
A
Thinking Skill:
Correct Answer:
Page 2
Published December 2007. May reproduce for instructional and educational
purposes only; not for personal or financial gain.