Grade 08 Mathematics - EC: M08.C-G.1.1.3

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

Instructional activities designed to be integrated into planned lessons
Questions/activities that grow in complexity
Opportunities for differentiation for each student’s level of performance

Grade Levels

8th Grade

Course, Subject

Mathematics

Related Academic Standards / Eligible Content

M08.C-G.1.1.3 M08.C-G.1.1.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Activities

What will the coordinates be of A’ if A(2, 5) is translated down 2 and left 4?

In the accompanying diagram, which point may be the image of point W after a reflection in the x-axis?
1. A
2. B
3. C
4. D

Rectangle ABCD is drawn on the coordinate grid below. Write the coordinates of A’B’C’D’ the image of ABCD after a dilation of scale factor 2. Explain how you found your coordinates.

Triangle ABC is drawn on the coordinate plane below. Identify the coordinates of triangle A’B’C’ the image after a reflection over the x-axis. Explain how you found your coordinates.

Graph the triangle with vertices A(-2, 2), B(-6, 2), and C(-2, 9), then graph and list the coordinates of triangle A’B’C’ under a 180° rotation. Write a rule that can be used for 180° rotations of any image.

Graph the quadrilateral with coordinates Q(-7, -3), R(-2, -2), S(-4, -7), T(-9, -8).
1. Graph and list the coordinates of Q’R’S’T’ after .
2. Write a rule that can be used to find the coordinates of the image.
3. Explain how to find the coordinates using the graph.

Answer Key/Rubric

A’(-2, 3)

A’(6, 4); B’(6, -6); C’(-10, -6); D’(-10, 4)
Acceptable explanations may include, but are not limited to:
Identify the coordinates of ABCD
Multiply the coordinates of ABCD by 2, the scale factor

A’(0, -6); B’(4,0); C’(-4, 3)
Acceptable explanations may include, but are not limited to:

To reflect a point over a line, you count to the line of reflection and then repeat that again on the other side
To find A’: count down 6 units to get to the x-axis, then count down another 6 units to get to (0, -6)
To find B’: it sits on the line of reflection so it will not move
To find C’: count up 3 units to the x-axis, then count up 3 more to get to (-4, 3)
To reflect over the x-axis, the x coordinate will remain the same but the y-coordinate will be opposite

A’(2, -2); B’(6, -2); C’(2, -9)

Rule:

Answers as follows:
1. Q’(-2, 0); R’(3, 1); S’(1, -4); T’(-4, -5)

Rule:
To find the coordinates using the graph: Start at one point and move 5 units to the right because it is a positive 5, then move up 3 units because it is also positive, plot your new point there. Continue for each point.