CC GeoB Unit 2 : The Coordinate Plane Practice Test

Transcription

1 Class: Date: CC GeoB Unit 2 : The Coordinate Plane Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Graph y = 3 4 x + 3. a. c. b. d. 2. Write an equation for the horizontal line that contains point E( 3, 1). a. x = 3 b. x = 1 c. y = 3 d. y = 1 1

2 3. Which diagram shows the most useful positioning of a square in the first quadrant of a coordinate plane? a. c. b. d. 4. Is the line through points P(0, 1) and Q( 4, 4) parallel to the line through points R(1, 3) and S( 5, 5)? Explain. a. No, the lines have unequal slopes. b. Yes; the lines have equal slopes. c. No, one line has slope, the other has no slope. d. Yes; the lines are both vertical. 2

3 5. Graph 6x 8y = 48. a. c. b. d. 6. Write an equation for the line perpendicular to y = 5x 14 that contains ( 4, 2). a. y 2 = 5(x + 4) c. y 4 = 1 (x + 2) 5 b. y 2 = 1 (x + 4) d. x 2 = 5(y + 4) 5 7. Is the line through points P(6, 4) and Q(8, 6) perpendicular to the line through points R( 8, 5) and S( 10, 3)? Explain. a. No, their slopes are not reciprocals. b. No, their slopes are not opposite reciprocals. c. Yes; their slopes are equal. d. Yes; their slopes have product 1 3

4 8. Which diagram shows the most useful positioning and accurate labeling of an isoscles trapezoid in the coordinate plane? a. c. b. d. 9. Write an equation in slope-intercept form of the line through points S(1, 4) and T(4, 2). a. y = 2x + 6 c. y = 2x 6 b. y = 2x 6 d. y = 2x Write an equation in point-slope form of the line through point J( 6, 9) with slope 8. a. y 9 = 8( x 6) c. y + 9 = 8( x 6) b. y 9 = 8( x + 6) d. y 9 = 8( x + 6) 11. Which two lines are parallel? I. 3y = 2x 3 II. 3y = 4 2x III. 4y 3x = 1 a. I and II c. II and III b. I and III d. No two of the lines are parallel. Short Answer and 2 are supplementary angles. m 1 = x 18, and m 2 = x Find the measure of each angle. 4

5 13. Find the perimeter of ABC with vertices A( 1, 3), B(2, 3), and C( 1, 1). 14. M(7, 7) is the midpoint of RS. The coordinates of S are (10, 6). What are the coordinates of R? 15. In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C? 16. A high school soccer team is going to Columbus 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 8.7 miles.) 17. The Frostburg-Truth bus travels from Frostburg Mall through the City Center to Sojourner Truth Park. The mall is 5 miles east and 4 miles north of the City Center. Truth Park is 2 miles west and 4 miles south of the Center. How far is it from Truth Park to the Mall to the nearest tenth of a mile? 18. Find the coordinates of the midpoint of the segment whose endpoints are H(7, 12) and K(5, 4). 19. For the parallelogram, find coordinates for P without using any new variables. 5

6 20. Find AD. 21. The vertices of the trapezoid are the origin along with A(4u, 4v), B(4w, 4v), and C(4x, 0). Find the midpoint of the midsegment of the trapezoid. 22. SQ bisects RST, and m RSQ = 4x 2. Write an expression for RST. The diagram is not to scale. 23. If EF = 2x 11, FG = 3x 9, and EG = 25, find the values of x, EF, and FG. The drawing is not to scale. 24. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale. 6

7 25. MO bisects LMN, m LMO = 7x 30, and m NMO = 2x Solve for x and find m LMN. The diagram is not to scale. 7

8 CC GeoB Unit 2 : The Coordinate Plane Practice Test Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: Graphing Lines TOP: 3-6 Example 1 KEY: slope-intercept form graphing 2. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: Writing Equations of Lines TOP: 3-6 Example 6 KEY: vertical line 3. ANS: C PTS: 1 DIF: L2 REF: 6-6 Placing Figures in the Coordinate Plane OBJ: Naming Coordinates NAT: NAEP 2005 G4d KEY: algebra coordinate plane rectangle square 4. ANS: A PTS: 1 DIF: L2 REF: 3-7 Slopes of Parallel and Perpendicular Lines OBJ: Slope and Parallel Lines TOP: 3-7 Example 1 KEY: slopes of parallel lines graphing parallel lines 5. ANS: C PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: Graphing Lines TOP: 3-6 Example 2 KEY: graphing standard form of a linear equation 6. ANS: B PTS: 1 DIF: L2 REF: 3-7 Slopes of Parallel and Perpendicular Lines OBJ: Slope and Perpendicular Lines TOP: 3-7 Example 5 KEY: slopes of perpendicular lines perpendicular lines 7. ANS: B PTS: 1 DIF: L2 REF: 3-7 Slopes of Parallel and Perpendicular Lines OBJ: Slope and Perpendicular Lines TOP: 3-7 Example 4 KEY: slopes of perpendicular lines perpendicular lines 8. ANS: C PTS: 1 DIF: L3 REF: 6-6 Placing Figures in the Coordinate Plane OBJ: Naming Coordinates NAT: NAEP 2005 G4d KEY: algebra coordinate plane isosceles trapezoid kite 9. ANS: C PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate Plane OBJ: Writing Equations of Lines KEY: slope-intercept form slope 10. ANS: B PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane OBJ: Writing Equations of Lines TOP: 3-6 Example 4 KEY: point-slope form 1

9 11. ANS: A PTS: 1 DIF: L2 REF: 3-7 Slopes of Parallel and Perpendicular Lines OBJ: Slope and Parallel Lines TOP: 3-7 Example 2 KEY: slopes of parallel lines parallel lines SHORT ANSWER 12. ANS: 1 = 46, 2 = 134 PTS: 1 DIF: L3 REF: 1-6 Measuring Angles OBJ: Identifying Angle Pairs NAT: NAEP 2005 M1e NAEP 2005 M1f NAEP 2005 G3g KEY: supplementary angles 13. ANS: 12 units PTS: 1 DIF: L2 REF: 1-9 Perimeter, Circumference, and Area OBJ: Finding Perimeter and Circumference NAT: NAEP 2005 M1c NAEP 2005 M1h ADP I.4.1 ADP J.1.6 ADP K.8.1 ADP K.8.2 TOP: 1-9 Example 3 KEY: perimeter triangle coordinate plane Distance Formula 14. ANS: (4, 8) PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane OBJ: Finding the Midpoint of a Segment NAT: NAEP 2005 M1e ADP J.1.6 ADP K.10.3 TOP: 1-8 Example 4 KEY: coordinate plane Midpoint Formula 15. ANS: (b, a) PTS: 1 DIF: L2 REF: 6-6 Placing Figures in the Coordinate Plane OBJ: Naming Coordinates NAT: NAEP 2005 G4d TOP: 6-6 Example 2 KEY: coordinate plane algebra rectangle 16. ANS: Ê 5, 5 ˆ 43.5 miles Ë Á 2, PTS: 1 DIF: L3 REF: 1-8 The Coordinate Plane OBJ: Finding Distance on the Coordinate Plane NAT: NAEP 2005 M1e ADP J.1.6 ADP K.10.3 TOP: 1-8 Example 2 KEY: Distance Formula coordinate plane word problem problem solving 17. ANS: 10.6 miles PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane OBJ: Finding Distance on the Coordinate Plane NAT: NAEP 2005 M1e ADP J.1.6 ADP K.10.3 TOP: 1-8 Example 2 KEY: coordinate plane Distance Formula word problem problem solving 2

10 18. ANS: (6, 8) PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane OBJ: Finding the Midpoint of a Segment NAT: NAEP 2005 M1e ADP J.1.6 ADP K.10.3 TOP: 1-8 Example 3 KEY: coordinate plane Midpoint Formula 19. ANS: (a + c, b) PTS: 1 DIF: L2 REF: 6-6 Placing Figures in the Coordinate Plane OBJ: Naming Coordinates NAT: NAEP 2005 G4d TOP: 6-6 Example 2 KEY: parallelogram coordinate plane algebra 20. ANS: 15 PTS: 1 DIF: L2 REF: 1-5 Measuring Segments OBJ: Finding Segment Lengths NAT: NAEP 2005 M1e NAEP 2005 M1f ADP I.2.1 TOP: 1-5 Example 1 KEY: segment segment length 21. ANS: (u + w + x, 2v) PTS: 1 DIF: L3 REF: 6-7 Proofs Using Coordinate Geometry OBJ: Building Proofs in the Coordinate Plane NAT: NAEP 2005 G4d KEY: algebra coordinate plane isosceles trapezoid midsegment 22. ANS: 8x 4 PTS: 1 DIF: L3 REF: 1-7 Basic Constructions OBJ: Constructing Bisectors NAT: NAEP 2005 G3b ADP K.2.2 ADP K.2.3 TOP: 1-7 Example 4 KEY: angle bisector 23. ANS: x = 9, EF = 7, FG = 18 PTS: 1 DIF: L2 REF: 1-5 Measuring Segments OBJ: Finding Segment Lengths NAT: NAEP 2005 M1e NAEP 2005 M1f ADP I.2.1 TOP: 1-5 Example 2 KEY: segment segment length 24. ANS: x = 8, ST = 56 PTS: 1 DIF: L2 REF: 1-5 Measuring Segments OBJ: Finding Segment Lengths NAT: NAEP 2005 M1e NAEP 2005 M1f ADP I.2.1 TOP: 1-5 Example 3 KEY: segment segment length midpoint multi-part question 3

11 25. ANS: x = 13, m LMN = 122 PTS: 1 DIF: L2 REF: 1-7 Basic Constructions OBJ: Constructing Bisectors NAT: NAEP 2005 G3b ADP K.2.2 ADP K.2.3 TOP: 1-7 Example 4 KEY: angle bisector 4