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Grade 8 Mathematics EOG (GSE) Quiz Answer KeyGeometry - (MGSE8.G.1 ) Verify Experimentally

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

1)

Which transformation shows a translation of 3 units to the right?

A)

B)

C)

D)

Explanation:The solution is B. The "P" in choice B has been translated 3 units to the right.

2)

Describe the transformation.

A) reflection across the y-axis

B) reflection across the x-axis

C) translation 4 units to the right

D) reflection across the line y = x



Explanation: The transformation is a Reflection across the y-axis. If the graph was folded along the y-axis, the vertices of the triangle would

correspond to one another.

3) Which type of transformation does NOT result in a figure that is congruent to the original one?

A) dilation

B) reflection

C) rotation

D) translation

Explanation:Solution: Dilation. A dilation changes the size of the original figure. The resulting figure is similar to the original one.

4)


A) translation 6 units down

B) translation 2 units down

C) reflection across the x-axis

D) reflection across the y-axis

Explanation:The transformation is a Reflection across the x-axis. If the graph was folded along the x-axis, the vertices of the triangle wouldcorrespond to each other.



5)


A) Translation 2 units down

B) Reflection across y = -1

C) Reflection across the x-axis

D) Reflection across the y-axis

Explanation:The transformation is a Reflection across the x-axis. If the graph was folded along the x-axis, the A's will match up.

6)

Which transformation shows a translation 4 units down?

A)

B)

C)

D)

Explanation:The solution is C. The "P" in choice C has been translated 4 units down.

7) If you rotate a right triangle, what feature of the triangle changes?

A) leg lengths

B) angle measures

C) length of hypotenuse



D) position of the triangle

Explanation:When transforming a figure using rotations, the angles and sides keep the same measure. The only thing that changes is the positionof the triangle .

8)

The angle is to be reflected over the line shown. What would be the measure of the reflected angle?

A) It would have the same measure as the original angle.

B) It would have half the measure of the original angle.

C) It would have double the measure of the original angle.

D) There is not enough information to know the measure of the reflected angle.

Explanation:A reflection across a line is a rigid transformation. Therefore the shape of the original object will not change. Because of this, youknow that it would have the same measure as the original angle.

9)

The line segment is to be reflected over the line shown. What would be the length of the reflected line segment?

A) It would have the same length as the original line segment.

B) It would have half the length of the original line segment.

C) It would have double the length of the original line segment.

D) There is not enough information to know the length of the original line segment.



Explanation:A reflection across a line is a rigid transformation. Therefore the shape of the original object will not change. Because of this, youknow that it would have the same length as the original line segment.



10)

The triangle shown is translated to the left 3. What are the new coordinates of point B?

A) (2, 7)

B) (5, 4)

C) (-1, 4)

D) (2, 1)

Explanation:(-1, 4)When a shape is translated to the left or right the only values that change are the x-coordinates. The y-coordinates remain the same.If the point is translated to the left, then subtract the value from the x-coordinate, if the point is translated to the right then add tothe x-coordinate.

11)




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.

12)

The graph shows a rectangle that has been translated. Which statement is FALSE?

A) The angles of the rectangle remained 90°.B) The parallel lines of the rectangle remained parallel.

C) The segments of the rectangle remained the same length.

D) The rectangle retained its same position on the coordinate plane.

Explanation:When transforming a figure using rotations, reflections, and translations, the angles and sides keep the same measure and parallellines remain parallel. The only thing that changes is its position in the coordinate plane. Therefore the only false statement is "therectangle retained its same position on the coordinate plane."

13)



Line l and Line m are parallel lines that have been rotated 180°. The resulting images are show as l' and m'. How can you describe l'and m'?

A) Skew lines

B) Parallel lines

C) Vertical lines

D) Intersecting lines

Explanation:Lines l' and m' have the same slope. Therefore they are parallel lines.



14)

Line j and Line k are parallel lines that have been translated. The resulting images are show as j' and k'. How can you describe j' andk'?

A) Skew lines

B) Parallel lines

C) Horizontal lines


Explanation:Lines j' and k' have the same slope. Therefore they are parallel lines.

15) If a pair of parallel lines are rotated, which is true?

A) The lines remain parallel only if rotated 180°.B) The lines remain parallel only if rotated 360°.C) Rotated parallel lines always remain parallel lines.

D) Rotating parallel lines result in perpendicular lines.

Explanation:Rotated parallel lines remain parallel lines.

Rotation is a rigid transformation, so the lines remain parallel.

16)



Line l and Line m are parallel lines that have been reflected across the origin;. The resulting images are show as l' and m'. How canyou describe l' and m'?

A) Skew lines

B) Parallel lines

C) Horizontal lines



17)



Line l and Line m are parallel lines that have been translated. The resulting images are show as l' and m'. How can you describe l'and m'?

A) Skew lines

B) Parallel lines

C) Vertical lines



18)



Line j and Line k are parallel lines that have been rotated about the origin. The resulting images are shown as j' and k'. How can youdescribe j' and k'?

A) Skew lines

B) Parallel lines

C) Horizontal lines





19)

Line l and Line m are parallel lines that have been reflected across the x-axis;. The resulting images are show as l' and m'. How canyou describe l' and m'?

A) Skew lines

B) Parallel lines

C) Vertical lines



20) If a pair of perpendicular lines are rotated, which is true?

A) Rotating perpendicular lines result in parallel lines.

B) The lines remain perpendicular only if rotated 180°.C) The lines remain perpendicular only if rotated 360°.D) Rotated perpendicular lines always remain perpendicular lines.

Explanation:Rotated perpendicular lines always remain perpendicular lines.

Rotation is a rigid transformation, so the lines remain perpendicular.

21)



Line l and Line m are parallel lines that have been reflected across the y-axis;. The resulting images are show as l' and m'. How canyou describe l' and m'?

A) Skew lines

B) Parallel lines

C) Vertical lines



22) AB has endpoints at (-1, -1) and (-2, -4). Its transformation A'B' has endpoints at (-2, -2) and (-4, -8). What type of transformationoccurred? Are lengths of segments affected by this type of transformation? Justify.

A) rotation; no; The lengths of the two segments are the same.

B) reflection; yes; The length of segment A'B' is longer than the original segment AB.

C) dilation by a scale factor of 2; yes; The length of segment A'B' is longer than the original segment AB.

D) dilation by a scale factor of 1

2; The length of segment A'B' is shorter than the original segment AB.

Explanation:dilation by a scale factor of 2; yes; The length of segment A'B' is longer than the original segment AB.

Find the length of each segment by using the distance formula:



d = (x2 - x1)2 + (y2 - y1)

2

The length of AB is 10 , which is about 3.16. The length of A'B' is 40 , which is about 6.32. The transformed segment is twice

the length of the original segment. This makes sense because the dilation of the line is by a scale factor of 2.



23)

Line J and Line K are parallel lines that have been rotated 90°. The resulting images are show as j' and k'. How can you describe j'and k'?

A) Skew lines

B) Parallel lines

C) Horizontal lines



24)



The line segment shown is reflected over the x-axis. What are the new coordinates of point B?

A) (4, 3)

B) (-4, 3)

C) (4, -3)

D) (-4, -3)

Explanation:When a line is reflected across the x-axis. The y-coordinates will change signs. Any positive y's will become negative and anynegative y's will become positive. The magnitude will not change. x-coordinates will not change. The point (4, 3) will become (4, -3)

25)



The triangle shown rotated 90° counterclockwise about the origin. What are the new coordinates of point A?A) (1, 2)

B) (-2, 1)

C) (2, 1)

D) (-2, -1)

Explanation:When a solid is rotated 90° around the origin the edges of the rotated solid are perpendicular to the corresponding original edge. Soa point (x, y) becomes (-y, x). Therefore, (1, -2) will become (2, 1)

26)



The triangle shown is reflected across the origin. What are the new coordinates of point B?

A) (4, 2)

B) (2, 4)

C) (-4, -2)

D) (-2, -4)

Explanation:When a shape is reflected about the origin the image of (x, y) is (-x, -y). No magnitudes change only signs. Therefore (2, 4) willbecome (-2, -4)

27) Lily graphs segment LM. Then, she reflects the segment across the y-axis. Which statement compares the lengths of the segmentLM and its transformation L'M' correctly?

A) LM = L'M'

B) LM < L'M'

C) LM > L'M'

D) L'M' < LM

Explanation:LM = L'M'

A reflection is a rigid transformation. A rigid transformation does not affect the length of a line segment.



28)

The line segment shown is rotated 90° about the origin (counterclockwise). What are the new coordinates of point A?A) (2, 1)

B) (-2, 1)

C) (-2, -1)

D) (1, 2)

Explanation:When a line segment is rotated 90° around the origin the new segment is perpendicular to the original one. So the point (x, y)becomes (-y, x). Therefore, (1, -2) will become (2, 1)

29)



The line segment shown is rotated 90° clockwise about the origin. What are the new coordinates of point B?A) (3, -4)

B) (-3, 4)

C) (-4, 3)

D) (-4, -3)

Explanation:When a line segment is rotated around the origin the new segment is perpendicular to the original one. So the point (x, y) becomes(y,-x). Therefore, (4, 3) will become (3, -4)

30)



AB is a translation of CD. To the nearest tenth, what is the length of each segment? Describe the effect of a translation on the lengthof a line segment.

A) AB is about 11.5 units; CD is about 10 units. A translated segment is longer than the original segment.

B) AB is about 10.5 units; CD is about 11.5 units. A translated segment is shorter than the original segment.

C) AB is about 11.3 units; CD is about 11.3 units. The length of a translated segment is the same as the original segment.

D) AB is about 12.5 units; CD is about 12.5 units. The length of a translated segment is the same as the original segment.

Explanation:AB is about 11.3 units; CD is about 11.3 units. The length of the translated segment is the same as the original segment.

Use the distance formula to find the length of both segments.

d = (x2 - x1)2 + (y2 - y1)

2

Substitute (-5, -1) and (3,7) into the formula fo AB.Substutitue (-2, 1) and (6,9) into the formula for CD.Simplifying: Both segments have a length of about 11.3 units. This proves that a translation has no effect on the length of a linesegment. It is a rigid transformation.

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