Answers GCSS_GA-Geometry Concepts and Connections_ICUnit Test

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On a coordinate plane, 5 trapezoids are shown. Trapezoid L M N P is in quadrant 2 and has points (negative 2, 3), (negative 2, 6), (negative 1, 6), and (negative 1, 4). Trapezoid B is reflected in quadrant 2. Trapezoid C is reflected across the y-axis. Trapezoid D is reflected into quadrant 4. Trapezoid A is reflected across the x-axis.

figure A

figure B

figure C

figure D

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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).

T4, –4(x, y)

T–4, –4(x, y)

T2, –4(x, y)

T–2, –4(x, y)

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).

rx-axis(x, y) → (–x, y)

ry-axis(x, y) → (–x, y)

rx-axis(x, y) → (x, –y)

ry-axis(x, y) → (x, –y)

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

(–4, 3)

(4, –3)

(–3, –4)

(3, 4)

On a coordinate plane, 3 triangles are shown. Triangle A B C has points (5, negative 5), (1, negative 2), (1, negative 5). Triangle A prime B prime C prime has points (5, 5), (1, 2), (1, 5). Triangle A double-prime B double-prime C double prime has points (negative 1, 3), (negative 5, 0), (negative 5, 3).

Translation of negative 6 units x, negative 2 units y composition reflection across the x-axis

Reflection across the x-axis composition translation of negative 6 units x, negative 2 units y

Translation of negative 6 units x, negative 2 units y composition 90 degree rotation about point 0

90 degree rotation about point 0 translation of negative 6 units x, negative 2 units y

A composition of transformations maps ΔKLM to ΔK"L"M".

a 90° rotation about point L

a 270° rotation about point L

a 90° rotation about point P

a 270° rotation about point P

What mistakes did he make? Select two options.

He applied the reflection to the pre-image first.

He applied the rotation to the pre-image first.

He changed the size of the figure instead of just applying a rotation.

He used point P as the center of rotation.

He used an incorrect angle of rotation around point P.

A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation?

T1, –9(x, y)

T–1, –9(x, y)

T–9, 1(x, y)

T–9, –1(x, y)

Square PQRS is transformed as shown on the graph.

R0, 90°

R0, 180°

R0, 270°

R0, 360°

Triangle ABC was transformed to create triangle DEF.

corresponds to because they are about the same length.

corresponds to because they are in the same position.

corresponds to because the transformation is isometric.

corresponds to because the length is not preserved.

Which rules could describe the rotation? Select two options.

R0, 90°

R0, 180°

R0, 270°

(x, y) → (–y, x)

(x, y) → (y, –x)

A transformation of ΔDEF results in ΔD'E'F'.

The transformation is a dilation.

The transformation is a reflection.

The transformation is a rotation.

The transformation is a translation.

Figure R S T U V is reflected across a point of reflection n to form R prime S prime T prime U prime V prime. Figure R prime S prime T prime U prime V prime is rotated 270 degrees about point P to form R double-prime S double-prime T double-prime U double-prime V double-prime

a reflection across line n followed by a translation down and to the right

a reflection across line n followed by a 270° rotation about point P

a translation down followed by a 270° rotation about point P

a translation down followed by a reflection across line n

A point has the coordinates (m, 0) and m ≠ 0.Which reflection of the point will produce an image located at (0, –m)?

a reflection of the point across the x-axis

a reflection of the point across the y-axis

a reflection of the point across the line y = x

a reflection of the point across the line y = –x

A regular decagon has 10 sides.

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).

Correct. He transformed the triangle according to the rule (x, y) → (–y, x).

Incorrect. He transformed the triangle according to the rule (x, y) → (y, –x)

Incorrect. He transformed the triangle according to the rule (x, y) → (–y, –x)

Incorrect. He transformed the triangle according to the rule (x, y) → (–x, –y)

Polygon LMNOP was transformed to create polygon L'M'N'O'P'.

Angle

Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Select two options.

The rule for the translation can be written as T–3, 1(x, y).

The rule for the translation can be written as T–1, 3(x, y).

The rule for the translation can be written as(x, y) → (x + 1, y – 3).

The rule for the translation can be written as(x, y) → (x – 3, y + 1).

Trapezoid ABCD has been translated 3 units to the right and 1 unit up.

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

(–1, –2)

(7, 1)

(–1, 7)

(–1, 1)

(7, –2)

Which diagram has all the correct lines of reflectional symmetry for the rectangle?

A rectangle is folded diagonally on both corners.

A rectangle is folded by a vertical and horizontal line going through its center.

A rectangle is folded 4 ways. It is folded horizontally, vertically, and diagonally on both corners.

A rectangle is folded 4 ways. It is folded diagonally at each midpoint of every side.

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