Virginia Mathematics Checkpoint Assessment GEOMETRY G.3. Topic: Reasoning, Lines, and Transformations

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1 Virginia Mathematics Checkpoint Assessment GEOMETRY G.3 Topic: Reasoning, Lines, and Transformations Standards of Learning Blueprint Summary Reporting Category Geometry SOL Number of Items Reasoning, Lines, and G.1(a-d), G.2(a-c), G.3(a-d), 18 Transformations G.4(a-g) Triangles G.5(a-d), G.6, G.7, G.8 14 Polygons, Circles, and Three- G.9, G.10, G.11(a-c), G.12, 18 Dimensional Figures G.13, G.14(a-d) Excluded from Testing None Number of Operational Items 50 Number of Field-Test Items 10 Total Number of Items on Test 60 Virginia Mathematics SOL Test Cut Scores Failing Scores Passing Scores Test Basic Proficient Advanced Minimum Minimum Minimum Minimum # correct % correct # correct % correct # correct % correct Math 3 16 of 40 40% 26 of 40 65% 36 of 40 90% Math 4 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 5 18 of 50 36% 31 of 50 62% 45 of 50 90% Math 6 16 of 50 32% 28 of 50 56% 45 of 50 90% Math 7 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 8 17 of 50 34% 31 of 50 62% 46 of 50 92% Algebra I n/a n/a 25 of 50 50% 45 of 50 90% Geometry n/a n/a 25 of 50 50% 44 of 50 88% Algebra II n/a n/a 27 of 50 54% 43 of 50 86% Geometry Checkpoint G.3 Page 1

2 Checkpoint Items 1. Directions: After showing your thinking, write your answer in the box. A is the endpoint of segment AC. B is the midpoint of segment AC. After showing your thinking, graph the missing endpoint. Write the coordinates of the missing endpoint in the box. Geometry Checkpoint G.3 Page 2

3 2. Directions: After showing your thinking, write your answer in the box. Given the coordinates of D( 2, 5) and M(6, 3), find the coordinates of the midpoint of DM. Geometry Checkpoint G.3 Page 3

4 3. Directions: After showing your thinking, write your answer in the box. Given the coordinates of S(3, 1) and T( 2, 0), find the slope of ST. Slope of ST = Geometry Checkpoint G.3 Page 4

5 4. Directions: After showing your thinking, graph a point on the coordinate plane using integral coordinates. Then, write the coordinates of your graphed point in the box. Given endpoints for ND to be N(1, 0) and D(7, 4), and given point R(5, 3), graph a point B so that RB ND. Geometry Checkpoint G.3 Page 5

6 5. Directions: After showing your thinking, write your answer in each box. Write the word parallel, perpendicular, or neither in each box. Given the equation for l 1 is 2x + 3y = 8, determine for each of the following whether they are parallel to l 1, perpendicular to l 1, or neither. a) y = 3 x b) y = 2 x 10 3 c) y = 2 x Geometry Checkpoint G.3 Page 6

7 6. Directions: Circle the box you want to select. Which type of symmetry does the figure on the coordinate plane have? Vertical line symmetry Horizontal line symmetry Point symmetry Geometry Checkpoint G.3 Page 7

8 7. Directions: Circle the box you want to select. Given the coordinates K( 1, 4), L( 4, 5), M( 3, 8), and after the result of a transformation the coordinates K (4, 1), L (5, 4), M (8, 3), determine what transformation occurred. Translation Reflection Rotation Dilation Geometry Checkpoint G.3 Page 8

9 8. Directions: Circle the box you want to select. A transformation mapped ABC to A B C. Which transformation occurred? Translation Reflection Rotation Dilation Geometry Checkpoint G.3 Page 9

10 9. Directions: Circle the box you want to select. You must select all correct answers. Select the ordered pair that would form a segment with the endpoint ( 1, 8) that has a length 5. (4, 4) (2, 4) (4, 8) Geometry Checkpoint G.3 Page 10

11 7. Directions: After showing your thinking, write your answer in the box. Your answer should be in simplest radical form. Given the endpoints (3, 6) and ( 9, 7), determine the length of the segment using the distance formula. Distance = Geometry Checkpoint G.3 Page 11

12 Checkpoint Solutions SOL G.3 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include a) investigating and using formulas for finding distance, midpoint, and slope; b) applying slope to verify and determine whether lines are parallel or perpendicular; c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods. Essential Knowledge and Skills a. Find the coordinates of the midpoint of a segment, using the midpoint formula b. Use a formula to find the slope of a line c. Compare the slopes to determine whether two lines are parallel, perpendicular, or neither d. Determine whether a figure has point symmetry, line symmetry, both or neither e. Given an image and preimage, identify the transformation that has taken place as a reflection, rotation, dilation, or translation f. Apply the distance formula to find the length of a line segment when given the coordinates of the endpoints Item Answer/Solution SOL/EKS Code 1 (4, 8) G.3aa 2 (2, 4) G.3aa *multiple correct answers* Possible answers are: (3, 0), (7, 6), (1, -3), (9, 9), (-1, -6), (-3, -9) G.3ab G.3bc 5a Perpendicular G.3bc 5b Neither G.3bc 5c Parallel G.3bc 6 Vertical line symmetry G.3cd 7 Rotation G.3de 8 Translation G.3de 9 (2, 4) and (4, 8) G.3af G.3af Essential Knowledge and Skills Find the coordinates of the midpoint of a segment, using the midpoint formula Find the coordinates of the midpoint of a segment, using the midpoint formula Use a formula to find the slope of a line Compare the slopes to determine whether two lines are parallel, perpendicular, or neither Compare the slopes to determine whether two lines are parallel, perpendicular, or neither Compare the slopes to determine whether two lines are parallel, perpendicular, or neither Compare the slopes to determine whether two lines are parallel, perpendicular, or neither Determine whether a figure has point symmetry, line symmetry, both or neither Given an image and preimage, identify the transformation that has taken place as a reflection, rotation, dilation, or translation Given an image and preimage, identify the transformation that has taken place as a reflection, rotation, dilation, or translation Apply the distance formula to find the length of a line segment when given the coordinates of the endpoints Apply the distance formula to find the length of a line segment when given the coordinates of the endpoints Geometry Checkpoint G.3 Page 12