congruence & geometric properties with equations...

4/3/2016 USATestprep, Inc.

http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=535 1/21

Coordinate Algebra EOC (GSE) QuizCongruence & Geometric Properties with Equations - (MGSE9‐12.G.CO.5) Draw Figure

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

Which transformation shows a reflection across the y-axis?

A)

B)

C)

D)

2)

If ΔMTV is reflected across the y-axis, what are the resulting coordinates of point M?

A) (-2, 5)

B) (-5, 2)

C) (5, -2)

D) (-2, -5)



3)

These two triangles can be shown to be congruent using which transformation?

A) reflection over the x-axis

B) reflection over the y-axis

C) translation right 4 units

D) rotation of 180°

4)

Which choice shows a reflection across the x-axis?

A)

B)

C)

D)

5)



Point M is located at (3, 7). If point M is translated 2 units to the left and 4 units down, what are the coordinates of M’?

A) (-1, 5)

B) (1, 3)

C) (5, 3)

D) (7, 5)

6)

When the blue trapezoid is translated to the green one, the new coordinates of the point (-2, 8) will be

A) (-4, 0).

B) (-8, 0).

C) (0, -8).

D) (-4, -8).



7)

Reflect pentagon ABCDE across the y-axis. What are the coordinates of B’?

A) (-5, 3)

B) (-4, 3)

C) (-3, 2)

D) (4, -3)

8)



Which composition of transformations can be used to show that figure 1 is congruent to figure 3?

A) rotation, then translation

B) rotation about (0, 0), then reflection

C) reflection, then rotation about (0, 0)

D) translation, then rotation about (0, 0)

9)



Which rectangle if translated 11 units right and 12 units down will result in rectangle E?

A) Rectangle A

B) Rectangle B

C) Rectangle C

D) Rectangle D

10)



Describe the transformation.

A) reflection across the x-axis

B) reflection across the y-axis

C) reflection across the line y = x

D) reflection across the line y = -x

11)

If polygon ABCD is translated 4 units to the right, in which quadrant will vertex C be?

A) I

B) II

C) IV

D) III



12)

The white shape can be transformed into the blue one using

A) a dilation, then a rotation.

B) a rotation, then a reflection.

C) a translation, then a dilation.

D) a reflection, then a translation.

13)

Find the coordinates of the vertices of the figure after the given transformation.

translation: (x, y)→(x - 4, y + 4)A) J'(1, 0), N'(5, 0), M'(5, 3), P'(2, 5)



B) J'(-2, 5), N'(2, 5), M'(2, 2), P'(-1, 0)

C) J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1)

D) J'(-1, 0), N'(-5, 0), M'(-5, -3), P'(-2, -5)



14)

The figure on the left has been transformed into the one on the right. Which transformation does this show?

A) (x', y') = (y, x)

B) (x', y') = (x, -y)

C) (x', y') = (-x, y)

D) (x', y') = (-y, x)

15)

Rotate trapezoid ABCD 90° clockwise around the origin. What are the coordinates of D’?

A) (-4, 2)

B) (4, -2)

C) (0, 4)

D) (4, 0)



16)

You are given rectangle ABCD on the grid shown and are told that the figure is reflected, but you are not told over which axis thishas occurred. Which COULD be the new coordinates of point D?

A) (4, -4)

B) (-6, -4)

C) (-2, -2)

D) (-1, -4)

17)

You are given rectangle ABCD on the grid shown and are told that the figure is moved two units. The person fails to tell you in whatdirection. Which COULD be the new coordinates of point D?

A) (4, -4)

B) (-6, -4)

C) (-2, -2)

D) (-1, -4)

18)




reflection across the x-axisA) U'(0, 5), P'(-1, 0), R'(3, -1), D'(3, 2)

B) U'(2, -4), P'(1, 1), R'(5, 2), D'(5, -1)

C) U'(-1, 3), P'(-2, 2), R'(2, 3), D'(2, 0)

D) U'(-4, -3), P'(-5, 2), R'(-1, 3), D'(-1, 0)

19)



Which rectangle if reflected over the x-axis and then translated 8 units right will result in rectangle E?

A) Rectangle A

B) Rectangle B

C) Rectangle C

D) Rectangle D



20)


reflection across the y-axisA) G'(4, 0), J'(3, -3), M'(0, -3)

B) G'(-1, 2), J'(-2, 5), M'(-5, 5)

C) G'(1, -2), J'(2, -5), M'(5, -5)

D) G'(0, 2), J'(-1, -1), M'(-4, -1)

21)



Which rectangle if translated 6 units right and 16 units down and the rotated 90° clockwise about the point (4, -11) will result inrectangle E?

A) Rectangle A

B) Rectangle B

C) Rectangle C

D) Rectangle D

22)



If Kite ABCD is reflected across the x-axis, what are the resulting coordinates of point A?

A) (1, -3)

B) (-3, 1)

C) (3, -1)

D) (-3, -1)

23)

When the blue trapezoid is translated to the green one, the new coordinates of the point (0, 0) will be

A) (-6, -2).

B) (-2, -8).

C) (-8, -6).

D) (-6, -8).



24)

Which translation can be used to prove that figures 2 and 3 are congruent?

A) (x, y) → (x, y - 4)

B) (x, y) → (x - 3, y + 1)

C) (x, y) → (x + 2, y)

D) (x, y) → (x + 1, y - 3)

25)

As shown in the graph, ΔGHI ≅ ΔG'H'I', since this is a vertical shift, and ΔG'H'I' ≅ ΔG''H''I'', since this is a horizontal shift.

We can also show that triangles GHI and G''H''I'' are congruent directly, by using the translation

A) (x, y) → (x + 3, y - 4).

B) (x, y) → (x - 3, y + 1).

C) (x, y) → (x + 2, y + 2).

D) (x, y) → (x + 4, y - 5).



26)

Triangles 1 and 2 can be shown to be congruent using the reflection

A) (x, y) → (-x, -y).

B) (x, y) → (-x, y).

C) (x, y) → (-y, x).

D) (x, y) → (y, x).

27)


translation: (x, y)→(x + 1, y - 1)



A) N'(0, -2), F'(4, 2), Q'(4, -2)

B) N'(-1, 1), F'(3, -3), Q'(3, 1)

C) N'(0, -1), F'(4, 3), Q'(4, -1)

D) N'(0, -5), F'(4, -1), Q'(4, -5)

28)

The figure on the left has been transformed into the one on the right. Which transformation does this show?

A) (x', y') = (y, x)

B) (x', y') = (x, y)

C) (x', y') = (-y, x)

D) (x', y') = (-y, -x)

29)

Which shows the original puzzle piece rotated 270° clockwise?

A)

B)

C)

D)

30) A triangle in Quadrant I is reflected over the y-axis, then over the x-axis, and then over the y-axis again. The new triangle, in



Quadrant IV, could ALSO have been obtained by using a single

A) dilation.

B) reflection.

C) rotation.

D) translation.

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