




Massachusetts Comprehensive Assessment System
2017, Grade 10 Mathematics
Question 17: 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: CCSS.Math.Content.HSGCO.A.5  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. 
Triangle KLM is shown on the coordinate grid below. Copy the axes, the labels, and triangle KLM exactly as shown onto the grid in your Student Answer Booklet.
 On the grid you copied into your Student Answer Booklet, draw triangle ${K}^{\text{'}}{L}^{\text{'}}{M}^{\text{'}}\text{,}$ the image of triangle KLM after it has been translated 8 units right and 3 units down. Be sure to label the vertices.
 On your grid, draw triangle ${K}^{\text{'}\text{'}}{L}^{\text{'}\text{'}}{M}^{\text{'}\text{'}}\text{,}$ the image of triangle ${K}^{\text{'}}{L}^{\text{'}}{M}^{\text{'}}\text{,}$ after it has been reflected over the xaxis. Be sure to label the vertices.
Point P(x, y) lies on triangle KLM. Point ${P}^{\text{'}\text{'}}$ is the image of point P after the transformations from part (a) and part (b) have been completed.
 Write an expression that represents the ycoordinate of point ${P}^{\text{'}\text{'}}$ in terms of y. Show or explain how you got your answer.

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 reflection or translation, and specifying a sequence of transformations that will carry a given figure onto another. The student performs two successive transformations of a triangle and describes the result algebraically as a single transformation. 
4 
3 
The student response demonstrates a good understanding of the Geometry concepts involved in drawing a transformed figure given a 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 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 a minimal understanding of the Geometry concepts involved in drawing a transformed figure given a 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 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: Geometry
 Question 20: Number and Quantity
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2017 Student Work Directory
Last Updated: July 2, 2018


