Name ________________________________________ Date ___________________ Class __________________
LESSON
4-1
Practice B
Congruence and Transformations
Apply the transformation M to the polygon with the given vertices.
Identify and describe the transformation.
1. M: (x, y) → (x − 2, y + 3)
2. M: (x, y) → (−x, y)
A(−1, −3), B(2, −1), C(2, −4)
P(−1, 2), Q(−2, −3), R(1, −2)
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3. M: (x, y) → (y, −x)
4. M: (x, y) → (2x, 2y)
G(−4, 3), H(−2, 3), J(−2, −1), K(−4, −1)
E(−2, 2), F(1, 1), G(2, 2)
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Determine whether the polygons with the given vertices are congruent.
5. A(−4, 4), B(−2, 4), C(−2, 2), D(−3, 1),
6. P(4, 4), Q(−4, 2), R(−2, 6);
E(−4, 2); P(2, 6), Q(4, 6), R(4, 4),
J(2, 2), K(−2, 1), L(−1, 3)
S(3, 3), T(2, 4)
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
4-4
Holt McDougal Geometry
Answers for the chapter Triangle Congruence
4-1 CONGRUENCE AND
2.
TRANSFORMATIONS
Practice A
1. A′(7, 7), B′(−2, 1), C′(3, −10); translation
4 units right and 3 units down
2. P′(2, −6), Q′(8, 2), R′(−4, −2); dilation
about (0, 0) with a scale factor of 2;
3. E′(−2, −2), F′(3, −4), G′(0, −5); reflection
across the x-axis
y-axis
4. R′(4, 3), S′(−2, −3), T′(−2, v2); rotation
90° clockwise with center (0, 0)
; reflection in the
3.
5. Yes; this is a translation 1 unit left and 2
units up.
6. Yes; this is a translation 2 units right and
4 units down.
7. No; the triangles are not congruent
because triangle GHL can be mapped
onto triangle PQR by a dilation with a
scale factor of 2 and a center of (0, 0).
about (0, 0), 90° clockwise
; rotation
4.
8. Yes; this is a reflection across the y-axis.
9. A′(−6, 0), B′(−3, 7), C′(−1, 6); this is a
translation 2 units to the left and 2 units
up
10. X′(−1, −2), Y′(−4, −1), Z′(−3, 1); this is a
rotation 180° clockwise with center (0, 0)
; dilation with
scale factor 2 and center (0, 0)
Practice B
1.
units left and 3 units up
5.
Yes, the pentagons are congruent
because pentagon ABCDE can be
mapped to pentagon PQRST by a
translation: (x, y) → (x + 6, y + 2).
6.
No, the triangles are not congruent
because triangle JKL can be mapped to
triangle PQR by a dilation with scale
factor 2 and a center of (0, 0).
Practice C
; translation 2
1. A′(2, 12), B′(−7, 6), C′(−2, −2); translation
1 unit left and 2 units up
2. A′(0.5, −1.5), B′(2, 0.5), C′(−1, −0.5);
dilation about (0, 0) with a scale factor of
1
2
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A31
Holt McDougal Geometry