




Massachusetts Comprehensive Assessment System
2013, Grade 10 Mathematics
Question 42: OpenResponse 

Reporting Category: Geometry Standard: 10.G.9  Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems. Standard: Mathematics.G.CO.1.05  Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 
Quadrilateral KLMN is shown on the coordinate grid below. Copy the coordinate grid and quadrilateral KLMN exactly as shown onto the grid in your Student Answer Booklet.Quadrilateral KLMN will be translated 9 units up. On your grid, draw quadrilateral K′L′M′N′, the image of quadrilateral KLMN after it has been translated 9 units up. Be sure to label the vertices.
Quadrilateral K′L′M′N′ will be reflected over the yaxis. On your grid, draw quadrilateral K″L″M″N″, the image of quadrilateral K′L′M′N′ after it has been reflected over the yaxis. Be sure to label the vertices.
 Explain whether a 180° rotation of quadrilateral KLMN about the origin would result in vertices with the same coordinates as K″L″M″N″.
Quadrilateral K″L″M″N″ will be rotated 90° clockwise about point M″ to create quadrilateral K′′′L′′′M′′′N′′′. What are the coordinates of point K′′′?

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Geometry concepts involved in drawing a transformed figure given a rotation, reflection, or translation, and specifying a sequence of transformations that will carry a given figure onto another. The student translates, reflects, and rotates a quadrilateral on the coordinate plane and determines the relationship between the images and the original quadrilateral. 
4 
3 
The student response demonstrates a good understanding of Geometry concepts involved in drawing a transformed figure given a rotation, reflection, or translation, and specifying a sequence of transformations that will carry a given figure onto another. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points. 
2 
The student response demonstrates a fair understanding of the Geometry concepts involved in drawing a transformed figure given a rotation, reflection, or translation, and specifying a sequence of transformations that will carry a given figure onto another. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates only minimal understanding of the Geometry concepts involved in drawing a transformed figure given a rotation, reflection, or translation, and specifying a sequence of transformations that will carry a given figure onto another. 
0 
The student response contains insufficient evidence of an understanding of the Geometry concepts involved in drawing a transformed figure given a rotation, reflection, or translation, and specifying a sequence of transformations that will carry a given figure onto another to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Statistics and Probability
 Question 20: Number and Quantity
 Question 21: Algebra and Functions
 Question 31: Algebra and Functions
 Question 41: Geometry
 Question 42: Geometry
Return to the MCAS 2013 Student Work Directory
Last Updated: November 18, 2014


