AnswersLJISD-TX-Geometry-1st 6WKSDirected Line Segments and Modeling

Directed Line Segments and Modeling — Cumulative exam Answers

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On a coordinate plane, a triangle has points R (negative 3, 4), T (negative 1, negative 4), and S (negative 4, negative 2).

Question illustration
A
(–4, 3)
B
(4, –3)
C
(–3, –4)
D
(3, 4)
23
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Triangle A B C is cut by line segment F G. Line segment F G goes from side A B to side A C. The length of B F is x + 6, the length of F A is x + 1, the length of C G is x + 3, and the length of G A is x minus 1.

Question illustration
A
1
B
3
C
6
D
9
24

Triangles D E F and D prime E prime F prime are connected at point E. Triangle D E F is rotated about point E to form triangle D prime E prime F prime.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation
25

Which points are vertices of the pre-image, rectangle ABCD? Select four options.

A
(–1, –2)
B
(7, 1)
C
(–1, 7)
D
(–1, 1)
E
(7, –2)
26

On a coordinate plane, a line goes through (negative 3, 2) and (0, 1). A point is at (3, 4).

Question illustration
A
y = –x + 5
Option A
B
y = –x + 3
Option B
C
y = 3x + 2
D
y = 3x − 5
27

On a coordinate plane, 2 triangles are shown. The first triangle has points F (3, 2), H (4, 5), G (1, 2). The second triangle has points F prime (negative 2, 3), H prime (negative 5, 4), G prime (negative 2, 1).

Question illustration
A
Correct. He transformed the triangle according to the rule (x, y) → (–y, x).
B
Incorrect. He transformed the triangle according to the rule (x, y) → (y, –x)
C
Incorrect. He transformed the triangle according to the rule (x, y) → (–y, –x)
D
Incorrect. He transformed the triangle according to the rule (x, y) → (–x, –y)
28

Point A has an x coordinate of −2 and lies in a circle with a center at (0, 0) and a radius of 5.

Question illustration
A
4.5
B
4.6
C
4.7
D
4.8
29

Which rules could describe the rotation? Select two options.

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
(x, y) → (–y, x)
E
(x, y) → (y, –x)
30

The proof that ΔRST ≅ ΔVST is shown.Given: ST is the perpendicular bisector of RV.Prove: ΔRST ≅ ΔVST

Question illustration
A
perpendicular bisector theorem
B
converse of the perpendicular bisector theorem
C
Pythagorean theorem
D
SSS congruence theorem
31

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

Question illustration
A
A ≅ Q because of the third angle theorem.
Option A
B
AB ≅ QN because they are both opposite a right angle.
C
BC ≅ NM because it is given.
D
C ≅ M because right angles are congruent.
Option D
32

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

A
27°
B
36°
C
54°
D
72°
33

Parallel lines s and t are cut by a transversal r. Which angles are alternate interior angles?

Question illustration
A
3 and 5
Option A
B
1 and 7
Option B
C
3 and 7
Option C
D
4 and 5
Option D
34

Given: HF || JK; HG ≅ JGProve: FHG ≅ KJG

Question illustration
A
FGH ≅ KGJ because vertical angles are congruent.
Option A
B
JKG ≅ HFG because vertical angles are congruent.
Option B
C
FHG ≅ JKG because right angles are congruent.
Option C
D
HFG ≅ KJG because alternate interior angles are congruent.
Option D
35

The truth table represents statements p, q, and r. pqr AT T T BT T F CT F T DT F F EF T T FF T F GF F T HF F F

A
r → (p ∧ q)
B
r → (p ∨ q)
C
(q ∧ r) → p
D
(q ∨ r) → p
36

In the diagram, which angles form a linear pair? Select three options.

A
RST and RSV
Option A
B
RST and TSU
Option B
C
RST and VSU
Option C
D
TSU and USV
Option D
E
TSU and RSV
Option E
37

Square PQRS is transformed as shown on the graph.

Question illustration
A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, 360°
38

On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).

Question illustration
A
x + 2y = 4
B
x + 2y = 8
C
2x + y = 4
D
2x + y = 8
39

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Question illustration
A
Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.
B
Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles.
C
Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.
D
Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.
40

On a coordinate plane, 2 quadrilaterals are shown. The first figure has points A (negative 2, 1), B (negative 4, 1), C (negative 4, 5), and D (negative 2, 4). Figure 2 has points A prime (2, 1), B prime (4, 1), C prime (4, 5), and D prime (2, 4).

Question illustration
A
rx-axis(x, y) → (–x, y)
B
ry-axis(x, y) → (–x, y)
C
rx-axis(x, y) → (x, –y)
D
ry-axis(x, y) → (x, –y)
41

Triangle EFG has vertices E(–3, 4), F(–5, –1), and G(1, 1). The triangle is translated so that the coordinates of the image are E’(–1, 0), F’(–3, –5), and G’(3, –3).

A
T4, –4(x, y)
B
T–4, –4(x, y)
C
T2, –4(x, y)
D
T–2, –4(x, y)

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Directed Line Segments and Modeling