Name: ________________________ Class: ___________________ Date: __________ ID: A 1 Geometry Module 4 Unit 1 Practice Exam Short Answer 1. Which point is the midpoint of AE ? 2. Find the midpoint of PQ. 3. Find the coordinates of the midpoint of the segment whose endpoints are H(7, 11) and K(3, 3). 4. M is the midpoint of CF for the points C(2, 1) and F(6, 7). Find MF. 5. M(3, 6) is the midpoint of RS . The coordinates of S are (4, 9). What are the coordinates of R? 6. T(8, 9) is the midpoint of CD . The coordinates of D are (8, 14). What are the coordinates of C? 7. Find the distance between points P(1, 1) and Q(6, 2) to the nearest tenth. 8. Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square. 9. The Frostburg-Truth bus travels from Frostburg Mall through the city’s center to Sojourner Truth Park. The mall is 4 miles east and 5 miles north of the city’s center. Truth Park is 5 miles west and 5 miles south of the city’s center. How far is it from Truth Park to the mall to the nearest tenth of a mile?
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Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Geometry Module 4 Unit 1 Practice Exam
Short Answer
1. Which point is the midpoint of AE?
2. Find the midpoint of PQ.
3. Find the coordinates of the midpoint of the segment whose endpoints are H(7, 11) and K(3, 3).
4. M is the midpoint of CF for the points C(2, 1) and F(6, 7). Find MF.
5. M(3, 6) is the midpoint of RS . The coordinates of S are (4, 9). What are the coordinates of R?
6. T(8, 9) is the midpoint of CD. The coordinates of D are (8, 14). What are the coordinates of C?
7. Find the distance between points P(1, 1) and Q(6, 2) to the nearest tenth.
8. Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square.
9. The Frostburg-Truth bus travels from Frostburg Mall through the city’s center to Sojourner Truth Park. The mall is 4 miles east and 5 miles north of the city’s center. Truth Park is 5 miles west and 5 miles south of the city’s center. How far is it from Truth Park to the mall to the nearest tenth of a mile?
Name: ________________________ ID: A
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10. A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high school and the stadium? (One unit 4.7 miles.)
11. Find the perimeter of the rectangle. The drawing is not to scale.
12. Ken is adding a ribbon border to the edge of his kite. Two sides of the kite measure 7.4 inches, while the other two sides measure 14.3 inches. How much ribbon does Ken need?
13. Jose wants to put a fence around his rectangular garden. His garden measures 34 feet by 35 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Jose need to enclose the garden and path?
14. Find the circumference of the circle to the nearest tenth. Use 3.14 for .
15. Find the circumference of the circle in terms of .
Name: ________________________ ID: A
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16. Find the perimeter of ABC with vertices A(–2, –5), B(4, –5), and C(–2, 3).
17. Find the perimeter of parallelogram ABCD with vertices A(–5, 6), B(2, 6), C(1, –2), and D(8, –2).
18. If the perimeter of a square is 120 inches, what is its area?
19. Find the area of a rectangle with base of 5 yd and a height of 4 ft.
Name: ________________________ ID: A
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20. Find the area of the circle in terms of .
21. Find the area of the circle to the nearest tenth. Use 3.14 for .
22. Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. The circle has a diameter of 12 inches.
23. The figure is formed from rectangles. Find the total area. The diagram is not to scale.
Name: ________________________ ID: A
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24. Write an expression that gives the area of the shaded region in the figure below. You do not have to evaluate the expression. The diagram is not to scale.
25. What is the slope of the line shown?
26. What is the slope of the line shown?
Name: ________________________ ID: A
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27. What is the slope of the line shown?
28. What is an equation in slope-intercept form for the line given?
29. Write the equation for the vertical line that contains point E(–3, 3).
30. Write the equation for the horizontal line that contains point G(6, 5).
31. Is the line through points P(–5, 6) and Q(6, 9) parallel to the line through points R(2, –1) and S(4, 5)? Explain.
32. What is the equation in point-slope form for the line parallel to y = 8x + 12 that contains P(–7, 8)?
33. What is the equation in point-slope form for the line parallel to y = –7x + 14 that contains J(4, 8)?
34. What is an equation in point-slope form for the line perpendicular to y = 3x + 5 that contains (–8, –1)?
35. In the coordinate plane, three vertices of rectangle PQRS are P(0, 0), Q(0, b), and S(c, 0). What are the coordinates of point R?
Name: ________________________ ID: A
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36. The vertices of the trapezoid are the origin along with A(4a, 4b), B(4c, 4b), and C(4d, 0). Find the midpoint of the midsegment of the trapezoid.
37. For the parallelogram, find coordinates for P without using any new variables.
ID: A
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Geometry Module 4 Unit 1 Practice ExamAnswer Section
SHORT ANSWER
1. ANS: 2
PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.1 Find the midpoint of a segment STA: MA.912.G.1.1TOP: 1-7 Problem 1 Finding the Midpoint KEY: segment length | segment | midpointDOK: DOK 2
2. ANS: (–1, 2)
PTS: 1 DIF: L2 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.1 Find the midpoint of a segment STA: MA.912.G.1.1TOP: 1-7 Problem 1 Finding the Midpoint KEY: coordinate plane | Midpoint Formula DOK: DOK 2
3. ANS: (5, 7)
PTS: 1 DIF: L2 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.1 Find the midpoint of a segment STA: MA.912.G.1.1TOP: 1-7 Problem 1 Finding the Midpoint KEY: coordinate plane | Midpoint Formula DOK: DOK 1
4. ANS:
13
PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.1 Find the midpoint of a segment STA: MA.912.G.1.1TOP: 1-7 Problem 1 Finding the Midpoint KEY: coordinate plane | Midpoint Formula DOK: DOK 1
5. ANS: (2, 3)
PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.1 Find the midpoint of a segment STA: MA.912.G.1.1TOP: 1-7 Problem 2 Finding an Endpoint KEY: coordinate plane | Midpoint Formula DOK: DOK 2
ID: A
2
6. ANS: (8, 4)
PTS: 1 DIF: L2 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.1 Find the midpoint of a segment STA: MA.912.G.1.1TOP: 1-7 Problem 2 Finding an Endpoint KEY: coordinate plane | Midpoint Formula DOK: DOK 2
7. ANS: 5.1
PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.2 Find the distance between two points in the coordinate planeSTA: MA.912.G.1.1 TOP: 1-7 Problem 3 Finding DistanceKEY: Distance Formula | coordinate plane DOK: DOK 2
8. ANS: 4 blocks
PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.2 Find the distance between two points in the coordinate planeSTA: MA.912.G.1.1 TOP: 1-7 Problem 4 Finding DistanceKEY: coordinate plane | Distance Formula | word problem | problem solvingDOK: DOK 2
9. ANS: 13.5 miles
PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.2 Find the distance between two points in the coordinate planeSTA: MA.912.G.1.1 TOP: 1-7 Problem 4 Finding DistanceKEY: coordinate plane | Distance Formula | word problem | problem solvingDOK: DOK 2
10. ANS:
5,52
, 23.5 miles
PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate PlaneOBJ: 1-7.2 Find the distance between two points in the coordinate planeSTA: MA.912.G.1.1 TOP: 1-7 Problem 4 Finding DistanceKEY: Distance Formula | coordinate plane | word problem | problem solving | midpointDOK: DOK 2
11. ANS: 218 feet
PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 1 Finding the Perimeter of a RectangleKEY: perimeter | rectangle DOK: DOK 1
ID: A
3
12. ANS: 43.4 in.
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 1 Finding the Perimeter of a RectangleKEY: perimeter | problem solving | word problem DOK: DOK 1
13. ANS: 162 ft
PTS: 1 DIF: L4 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 1 Finding the Perimeter of a RectangleKEY: perimeter | rectangle | word problem | problem solving DOK: DOK 2
14. ANS: 87.9 m
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 2 Finding CircumferenceKEY: circle | circumference DOK: DOK 2
15. ANS:
106 in.
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 2 Finding CircumferenceKEY: circle | circumference DOK: DOK 2
16. ANS: 24 units
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 3 Finding Perimeter in the Coordinate PlaneKEY: perimeter | triangle | coordinate plane | Distance Formula DOK: DOK 2
17. ANS: 34 units
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 3 Finding Perimeter in the Coordinate PlaneKEY: perimeter | coordinate plane | Distance Formula DOK: DOK 2
ID: A
4
18. ANS:
900 in.2
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 4 Finding Area of a RectangleKEY: area | square DOK: DOK 2
19. ANS:
60 ft2
PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 4 Finding Area of a RectangleKEY: area | rectangle DOK: DOK 1
20. ANS:
529 in.2
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 5 Finding Area of a CircleKEY: area | circle DOK: DOK 1
21. ANS: 171.9 in.2
PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 5 Finding Area of a CircleKEY: area | circle DOK: DOK 1
22. ANS:
30.9 in.2
PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 6 Finding Area of an Irregular ShapeKEY: circle | square | area DOK: DOK 2
23. ANS:
109 ft2
PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 6 Finding Area of an Irregular ShapeKEY: area | rectangle DOK: DOK 2
ID: A
5
24. ANS: A (20 4) (11 6)
PTS: 1 DIF: L2 REF: 1-8 Perimeter, Circumference, and AreaOBJ: 1-8.1 Find the perimeter or circumference of basic shapes STA: MA.912.G.2.5| MA.912.G.6.5 TOP: 1-8 Problem 6 Finding Area of an Irregular ShapeKEY: rectangle | area DOK: DOK 2
25. ANS: 4
PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate PlaneOBJ: 3-7.1 Graph and write linear equations TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope | linear graph | graph of lineDOK: DOK 2
26. ANS: 89
PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate PlaneOBJ: 3-7.1 Graph and write linear equations TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope | linear graph | graph of lineDOK: DOK 2
27. ANS:
35
PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate PlaneOBJ: 3-7.1 Graph and write linear equations TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope | linear graph | graph of lineDOK: DOK 2
28. ANS: y 4 / 9x (11 / 9)
PTS: 1 DIF: L4 REF: 3-7 Equations of Lines in the Coordinate PlaneOBJ: 3-7.1 Graph and write linear equations TOP: 3-7 Problem 4 Using Two Points to Write an Equation KEY: point-slope formDOK: DOK 2
29. ANS: x = –3
PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate PlaneOBJ: 3-7.1 Graph and write linear equations TOP: 3-7 Problem 5 Writing Equations of Horizontal and Vertical LinesKEY: vertical line DOK: DOK 2
ID: A
6
30. ANS: y = 5
PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate PlaneOBJ: 3-7.1 Graph and write linear equations TOP: 3-7 Problem 5 Writing Equations of Horizontal and Vertical LinesKEY: horizontal line DOK: DOK 2
31. ANS: No; the lines have unequal slopes.
PTS: 1 DIF: L2 REF: 3-8 Slopes of Parallel and Perpendicular LinesOBJ: 3-8.1 Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 1 Checking for Parallel Lines KEY: slopes of parallel lines | graphing | parallel lines DOK: DOK 2
32. ANS: y – 8 = 8(x + 7)
PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular LinesOBJ: 3-8.1 Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 2 Writing Equations of Parallel Lines KEY: slopes of parallel lines | parallel lines DOK: DOK 2
33. ANS: y – 8 = –7(x – 4)
PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular LinesOBJ: 3-8.1 Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 2 Writing Equations of Parallel Lines KEY: slopes of parallel lines | parallel lines DOK: DOK 2
34. ANS:
y + 1 = 13
(x + 8)
PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular LinesOBJ: 3-8.1 Relate slope to parallel and perpendicular lines TOP: 3-8 Problem 4 Writing Equations of Perpendicular Lines KEY: slopes of perpendicular lines | perpendicular lines DOK: DOK 2
35. ANS: (c, b)
PTS: 1 DIF: L2 REF: 6-8 Applying Coordinate GeometryOBJ: 6-8.1 Name coordinates of special figures by using their propertiesSTA: MA.912.G.1.1| MA.912.G.2.6| MA.912.G.3.3| MA.912.G.3.4| MA.912.G.4.8| MA.912.G.8.5TOP: 6-8 Problem 2 Using Variable Coordinates KEY: coordinate plane | algebra | rectangle DOK: DOK 2
ID: A
7
36. ANS: (a + c + d, 2b)
PTS: 1 DIF: L3 REF: 6-8 Applying Coordinate GeometryOBJ: 6-8.1 Name coordinates of special figures by using their propertiesSTA: MA.912.G.1.1| MA.912.G.2.6| MA.912.G.3.3| MA.912.G.3.4| MA.912.G.4.8| MA.912.G.8.5TOP: 6-8 Problem 2 Using Variable Coordinates KEY: algebra | coordinate plane | isosceles trapezoid | midsegment DOK: DOK 2
37. ANS: (a + c, b)
PTS: 1 DIF: L2 REF: 6-8 Applying Coordinate GeometryOBJ: 6-8.1 Name coordinates of special figures by using their propertiesSTA: MA.912.G.1.1| MA.912.G.2.6| MA.912.G.3.3| MA.912.G.3.4| MA.912.G.4.8| MA.912.G.8.5TOP: 6-8 Problem 2 Using Variable Coordinates KEY: parallelogram | coordinate plane | algebra DOK: DOK 2
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