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Coordinate Algebra EOC (GSE) Quiz Answer KeyCongruence & 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)

Explanation:IMAGES NEED TO SEPARATED - The solution is A. The "P" in choice A has been reflected across the y-axis.

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)

Explanation:Solution: (-2, 5). Reflecting the triangle across the y-axis will result in every x-coordinate becoming opposite.

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°

Explanation:reflection over the y-axis is correct. Since the orientation of the triangle changed it can not be a translation.

4)

Which choice shows a reflection across the x-axis?

A)

B)

C)

D)



Explanation: The solution is D. The "P" in choice C has been reflected across the x-axis.



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)

Explanation:(3 – 2 = 1, 7 – 4 = 3) The coordinates of M’ are (1, 3).

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).

Explanation:(-8, 0) is correct. Imagine lifting the blue one up and dropping it onto the green one.

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)

Explanation:The coordinates of B are (4, 3). After reflecting across the y-axis, the coordinates of B’ are (-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)

Explanation:Use reflection, then rotation about (0, 0) to do it. Reflect over the y-axis, then rotate clockwise.



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

Explanation:If rectangle B is translated 11 units right and 12 units down, it will map directly on top of rectangle E.

A figure can be moved anywhere in space to fit perfectly over another figure that is congruent to it by using three simple motions orcombination of motions:

Translation (slide)Rotation (turn)Reflection (flip)

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

Explanation:The transformation is a Reflection across the line y = x. If the graph was folded along the line y = x, the points of the two triangleswould correspond to each other.

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

Explanation:If you move the polygon four units to the right vertex C will go from (-3, 7) to (1,7). The result is in quadrant I.

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.

Explanation:A a rotation, then a reflection. The white shape is rotated to the yellow one, then the yellow one is reflected to the blue one.



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)

Explanation:The rule (x, y)→(x - 4, y + 4), means to translate the figure four points to the left and four points up. If we apply this rule to eachvertex of the figure, the resulting coordinates are J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1).

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)



Explanation:(x', y') = (x, -y) is correct. The x-values do not change, but the y-values take on opposite signs. This is a reflection in the x-axis.

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)

Explanation:The coordinates of D are (-4, 0). After rotating 90° clockwise around the origin, the coordinates of D’ are (0, 4).

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)

Explanation:The coordinates of point D are (-4, -4). Look for coordinates that have the sign of either the x or the y coordinate changed but notboth. Therefore the correct answer is (4, -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)

Explanation:The coordinates of point D are (-4, -4). Look for coordinates that have 2 either added or subtracted from either the x or the ycoordinate but not both. Therefore the correct answer is (-6, -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)

Explanation:When we reflect across the x-axis, the resulting image will be a mirror image with the x-axis as the line of symmetry. Therefore,U'(0, 5), P'(-1, 0), R'(3, -1), D'(3, 2) are the correct coordinates.

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

Explanation:If rectangle D is reflected over the x-axis and then translated 8 units right, it will map directly on top of rectangle E.



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)

Explanation:When we reflect across the y-axis, the resulting image will be a mirror image with the y-axis as the line of symmetry. Therefore, G'(1,-2), J'(2, -5), M'(5, -5) are the correct coordinates.



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

Explanation:If rectangle C is translated 6 units right and 16 units down and the rotated 90° clockwise about the point (4, -11), it will map directlyon top of rectangle E.



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)

Explanation:Solution: (-3, 1). Reflecting the kite across the x-axis will result in every y-coordinate becoming the opposite.

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).

Explanation:(-6, -8) is correct. Since the point (6, 8) ends up at (0, 0), we can see that we have to subtract 6 from the x and 8 from the y. Doingthis to the point (0, 0) results in (-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)

Explanation:(x, y) → (x, y - 4) is correct. For example, the point (-2, 1) in figure 2 becomes (-2, -3) in figure 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).

Explanation:(x, y) → (x - 2, y - 5) is correct. For example, the point (-2, 1) in GHI becomes (2, -4) in figure G''H''I''.

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).



Explanation:(x, y) → (-x, y). is correct. For example, the point (-3, 5) on triangle 1 goes to (3, 5) on triangle 2.

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)

Explanation:The rule (x, y)→(x + 1, y - 1), means to translate the figure one point to the right and one point down. If we apply this rule to eachvertex of the figure, the resulting coordinates are N'(0, -2), F'(4,2), Q'(4,-2).

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)

Explanation:(x', y') = (y, x) is correct. This is a reflection in the line y = x.

29)

Which shows the original puzzle piece rotated 270° clockwise?

A)

B)

C)

D)

Explanation:Puzzle piece C has been rotated 270° clockwise.



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

A) dilation.

B) reflection.

C) rotation.

D) translation.

Explanation:A single reflection over the x-axis from Quadrant I would have had the same result.

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