NAME: ____________________________DATE: _____________PERIOD: _______

Geometry

Fall Final Exam Review 2016

1. Find the coordinates of the midpoint of each side of the parallelogram.

2. Find the distance between the two points. Then find the midpoint of the line segment connecting the two

points. (5, –3), (–4, 7)

3. Prove that A(1, 1), B(3, 3), and C(5, 1) are the vertices of a right triangle.

4. has endpoints and Prove that the midpoint of lies in quadrant IV.

My Exam is on: ____________ This review is due on: ___________

5. Use the given vertices to graph . Classify . Then find its perimeter.

6. Write an equation in slope-intercept form for the line that passes through and is perpendicular to

the line described by .

7. Write the equation of the line that has y-intercept 4 and is parallel to .

8. Suppose the preimage for the transformation given by the rule has vertices

, , , , , and . Use the rule to determine the coordinates of

the corresponding vertices of the image.

Preimage

Image

9. Rotate this figure the given number of degrees counterclockwise about the origin. List the coordinates

of the vertices of the image.

10. Rotate the figure 90° about the origin. List the coordinates of the vertices of the image.

11. The vertices of are , and . Find the vertices of after a

composition of the transformation in the order they are listed.

Translation:

Reflection: in the -axis

12. A triangle with vertices , , and is reflected across the y-axis. Identify the

coordinates of the image of point Q.

Q’ ( , )

13. Identify the image of the point when A is reflected across the line .

A’ ( , )

S ( , ) T ( , ) U ( , ) V ( , )

S’ ( , ) T’ ( , ) U’ ( , ) V’ ( , )

J ( , ) K ( , ) L ( , ) M ( , ) N ( , )

J’ ( , ) K’ ( , ) L’ ( , ) M’ ( , ) N’ ( , )

A’ ( , ) B’ ( , ) C’ ( , )

A” ( , ) B” ( , ) C” ( , )

14. Graph the triangle whose vertices have the coordinates given below. Then draw its reflection in the x-axis.

(–7, 2), (–2, 2), (–6, 7)

15. Decide whether the transformation from Figure A to Figure B is a translation, reflection, or rotation.

16. Tell whether a rigid motion can move the solid figure onto the dashed figure. If so, describe the

transformation(s) that you can use. If not, explain why the figures are not congruent.

17. Identify the transformation(s) you can use to move figure A onto figure B.

I

J

K

N L

M

4 cm8 cm

6.9 cm

60°

30°

18. Determine whether the figure has line symmetry. If possible, identify the number of lines of symmetry.

19. Decide whether the figure has line symmetry and/or rotational symmetry. Identify the number of lines of

symmetry and/or the rotations that map the figure onto itself.

20. On the regular hexagon, draw all possible lines across which you can reflect the hexagon onto itself.

21. Find the length of . State the postulate or theorem you use.

22. Given , find the length of all unlabeled sides and the measure of all unlabeled angles.

23. In the figure below, . Find and m .

H

GF

7.2

75°

1.9

T

RS

24. Prove that the triangle with vertices , , is an isosceles triangle.

25.

26.

27.

28. Point R lies on the line segment joining P( -7, 8 ) and Q( 5, -4 ). If PR = RQ, what are the

coordinates of R?

29. One end of a line segment has the coordinates ( -3, -8 ). If the midpoint is ( 5, 8 ), then what are

the coordinates of the other endpoint?

30. Consider the point at .

a. Find the coordinates of , the image of after the transformation .

b. What type of transformation is ?

c. Find the coordinates of , the image of after the transformation .

d. Write a transformation rule to map to .

31. Use the figure below to answer parts a through c.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

a. Draw the image of the figure after a counterclockwise rotation

about the origin.

b. Draw the image of the figure from part a after the translation

.

c. Is the result from part b the same as the result of translating the

original figure using followed by rotating it

by counterclockwise about the origin? Explain your reasoning.

32. Find the measure of each of the numbered angles.

Explain your reasoning for each angle.

D E

FG

110°1 3

2

63°

4 5

33.

34.

35.

Fall Final Exam Review

Answer Section

1. ANS:

(–3, 3), , (2, 5),

2. ANS:

, (0.5, 2)

3. ANS:

Sample answer: Slope of . Slope of . Since and have negative

reciprocal slopes, the segments are perpendicular and meet at point B to form a right angle. Therefore,

is a right triangle.

4. ANS:

The midpoint of is The x-coordinate is positive, and the y-coordinate is

negative, so the point is in quadrant IV.

5. ANS:

rhombus; 20 units

6. ANS:

7. ANS:

8. ANS:

Preimage

Image

9. ANS:

10. ANS:

J’ ( 0, -3 ), K’ ( -3, -1 ), L’ ( -1, 2 ), M’ ( 2, 1 ), N’ ( 3, -2 )

11. ANS:

12. ANS:

13. ANS:

14. ANS:

15. ANS:

reflection

16. ANS:

No; a reflection maps two sides to congruent sides, but the other sides are not congruent.

17. ANS:

reflection

18. ANS:

yes; 1

19. ANS:

line symmetry; one line of symmetry

20. ANS:

21. ANS:

LM = 290; ASA Congruence

22. ANS:

; ;

; ;

23. ANS:

;

24. ANS:

A

B

C

1 2 3 4 5–1 x

1

2

3

4

5

–1

y

Two of the sides of the triangle are congruent, so is an isosceles triangle.

25. ANS:

x = 28

26. ANS:

x = 20

27. ANS:

x = 35

28. ANS:

(-1, 2)

29. ANS:

(13, 24)

30. ANS:

a.

b. The transformation is a rotation of about the origin.

c.

d. One possible transformation rule is . Answers can vary.

31. ANS:

a. The image of after rotating counterclockwise about the origin is . The vertices of the

image are , , and .

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

b. The vertices of the image of the translation under are , , and .

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

c. No; the vertices of the image of the original figure after translating it under

followed by rotating counterclockwise about the origin are , , and . The

vertices of the image after this sequence of transformations are not the same as the result from part b.

32. ANS:

Possible answer:

and the angle which measures are supplementary, so .

and the angle which measures are alternate interior angles, so .

The sum of the interior angles in a triangle is . .

and are alternate interior angles, so .

and are opposite angles in a parallelogram, so . Thus, .

33. a = 2

34. 46

35. x = 12