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Lesson Menu
Five-Minute Check (over Lesson 92) NGSSS Then/Now
New Vocabulary Key Concept Rotation Example
1 Draw a Rotation Key Concept Rotations in the
Coordinate Plane Example 2 Rotations in the
Coordinate Plane Example 3 Standardized Test
Example
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5-Minute Check 1
A. R'(2, 2), S'(1, 1) B. R'(0, 3), S'(5,
3) C. R'(3, 4), S'(1, 1) D. R'(3, 4), S'(5, 3)

1. A
2. B
3. C
4. D

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5-Minute Check 2
Find the coordinates of the figure under the
given translation.?ABC with vertices A(4, 3),
B(2, 1), and C(0, 5) under the translation (x,
y) ? (x 3, y 4)
A. A'(2, 1), B'(1, 3), C'(3, 1) B. A'(1,
1), B'(1, 3), C'(3, 1) C. A'(0, 5), B'(6, 3),
C'(4, 7) D. A'(1, 1), B'(2, 5), C'(5, 9)

1. A
2. B
3. C
4. D

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5-Minute Check 3
Find the coordinates of the figure under the
given translation.trapezoid LMNO with vertices
L(2, 1), M(5, 1), N(1, 5) and O(0, 2) under
the translation (x, y) ? (x 1, y 4)

1. A
2. B
3. C
4. D

A. L'(1, 5), M'(4, 5), N'(0, 1), O'(1,
2) B. L'(2, 6), M'(5, 7), N'(1, 0), O'(0,
3) C. L'(3, 3), M'(6, 2), N'(0, 8), O'(1,
6) D. L'(4, 4), M'(7, 5), N'(0, 1), O'(1, 4)
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5-Minute Check 4
A. (x 2, y 3) B. (x 2, y 2) C. (x 3, y
2) D. (x 3, y 2)

1. A
2. B
3. C
4. D

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5-Minute Check 5
The preimage of rectangle ABCD has vertices at
A(4, 5), B(4, 3), C(1, 3), and D(1, 5). Its
image has vertices at A'(1, 3), B'(1, 5),
C'(4, 5), and D'(4, 3). Write the ordered pair
that describes the transformation of the
rectangle.
A. (x, y) ? (x 3, y 2) B. (x, y) ? (x 3, y
2) C. (x, y) ? (x 2, y 3) D. (x, y) ? (x
2, y 3)

1. A
2. B
3. C
4. D

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NGSSS
MA.912.G.2.4 Apply transformations to polygons to
determine congruence, similarity, and symmetry.
Know that images formed by translations,
reflections, and rotations are congruent to the
original shape. Create and verify tessellations
of the plane using polygons. MA.912.G.2.6 Use
coordinate geometry to prove properties of
congruent, regular and similar polygons, and to
perform transformations in the plane.
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Then/Now
You identified rotations and verified them as
congruence transformations. (Lesson 47)

• Draw rotations.

• Draw rotations in the coordinate plane.

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Vocabulary

• center of rotation
• angle of rotation

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Concept
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Example 1
Draw a Rotation
Rotate quadrilateral RSTV 45 counterclockwise
about point A.

• Draw a segment from point R to point A.

• Locate point R' so that AR AR'.

• Repeat this process for points S, T, and V.

• Connect the four points to form R'S'T'V'.

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Example 1
Draw a Rotation
Quadrilateral R'S'T'V' is the image of
quadrilateral RSTV under a 45 counterclockwise
rotation about point A.
Answer
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Example 1
For the following diagram, which description best
identifies the rotation of triangle ABC around
point Q?
A. 20 clockwise B. 20 counterclockwise C. 90
clockwise D. 90 counterclockwise

1. A
2. B
3. C
4. D

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Concept
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Example 2
Rotations in the Coordinate Plane
Triangle DEF has vertices D(2, 1), E(1, 1),
and F(1, 1). Graph ?DEF and its image after a
rotation of 115 clockwise about the point G(4,
2).
First draw ?DEF and plot point G.
Draw a segment from point G to point D.
Repeat with points E and F.
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Example 2
Rotations in the Coordinate Plane
Answer ?D'E'F' is the image of ?DEF under a 115
clockwise rotation about point G.
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Example 2
Triangle ABC has vertices A(1, 2), B(4, 6), and
C(1, 6). Draw the image of ?ABC under a
rotation of 70 counterclockwise about the point
M(1, 1).

1. A
2. B
3. C
4. D

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Example 3
Hexagon DGJTSR is shown below. What is the image
of point T after a 90? counterclockwise rotation
about the origin? A (5, 3) B (5, 3) C (3,
5) D (3, 5)
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Example 3
Read the Test Item You are given a graph of
hexagon DGJTSR and asked to identify the
coordinates of the image of point T after a 90
counterclockwise rotation about the origin. Solve
the Test Item To find the coordinates of point T
after a 90?counterclockwise rotation about the
origin, multiply the y-coordinate by 1 and then
interchange the x- andy-coordinates. (x, y) ?
(y, x) (5, 3) ? (3, 5)
Answer The answer is C, (3, 5).
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Example 3
Triangle PQR is shown below. What is the image of
point Q after a 90 counterclockwise rotation
about the origin?
A. (5, 4) B. (5, 4) C. (5, 4) D. (4, 5)

1. A
2. B
3. C
4. D

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End of the Lesson