Minds On

Where am I?

Imagine you are playing a game where the goal is to identify the location of an object hidden on a Cartesian plane. You have placed your object on the Cartesian plane as indicated in the image. Your partner guesses the following location (-6, 8). Is your partner correct? Record your thinking about why this is not correct.

A Cartesian plane, with an image of a treasure chest in the first quadrant. One corner of the chest rests at (6,8).

What’s the point?

For each of the following, determine the coordinates of the point shown. Use a recording method of your choice and then click on ‘Answer’ to check your answers.

4-quadrant Cartesian plane with a dot indicating a coordinate at 5 on the x-axis and 4 on the y-axis.

Press ‘Answer’ to access the solution.

The answer is (5,4).
A Cartesian plane with the coordinates 0 on the x-axis and 7 on the y-axis.

Press ‘Answer’ to access the solution.

The answer is (0,7).
A Cartesian plane with the coordinates -2 on the x-axis and 3 on the y-axis.

Press ‘Answer’ to access the solution.

The answer is (-2,3).
A Cartesian plane with the coordinates at 9 on the x-axis and 0 on the y-axis.

Press ‘Answer’ to access the solution.

The answer is (9,0).
A 4-quadrant Cartesian plane with the coordinate selected at -6 on the x-axis and -4 on the y-axis.

Press ‘Answer’ to access the solution.

The answer is (-6, -4).
A Cartesian plane with the coordinates at 9 on the x-axis and -2 on the y-axis.

Press ‘Answer’ to access the solution.

The answer is (9,-2).
A Cartesian plane with the coordinates at 0 on the x-axis and -2 on the y-axis.

Press ‘Answer’ to access the solution.

The answer is (0,-2).

Action

Let’s play a matching game!

On each of these Cartesian planes, there is a 3 × 6 rectangle marked “original” and one image to compare. The coordinates of the original image are all A(3, 2), B(9, 2), C(9, 5), D(3, 5). Think about the correct transformation description. Include the coordinates as well as a note whether the new image is a translation, reflection, or rotation of the original one in your answer. Then, click on ‘Answer’ under each Cartesian plane to reveal the response.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(-2, 3), B'(-2, 9), C'(-5, 9), D'(-5, 3).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(-2, 3), B'(-2, 9), C' (-5, 9), D'(-5, 3). Answer: rotated CCW 90°.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(3, -2), B'(9, -2), C'(9, -5), D'(3, -5).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(3, -2), B'(9, -2), C'(9, -5), D'(3, -5). Answer: reflected in the x-axis.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(-3, 2), B'(-9, 2), C'(-9, 5), D'(-3,5).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(-3, 2), B'(-9, 2), C'(-9, 5), D'(-3,5). Answer: reflected in the y-axis.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(8, 11), B'(14, 11), C'(14, 14), D'(8,14).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(8, 11), B'(14, 11), C'(14, 14), D'(8,14). Answer: Translated 5 right and 9 up.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(-3, -2), B'(-9, -2), C'(-9, -5), D'(-3, -5).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(-3, -2), B'(-9, -2), C'(-9, -5), D'(-3, -5). Answer: rotated 180°.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(2, -3), B'(2, -9), C'(5, -9), D'(5, -3).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(2, -3), B'(2, -9), C'(5, -9), D'(5, -3). Answer: rotated CW 90°.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(-7, -3), B'(-1, -3), C'(-1, 0), D'(-7,0).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(-7, -3), B'(-1, -3), C'(-1, 0), D'(-7,0). Answer: Translated 10 left and 5 down.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(3, -11), C'(9, -11), C'(9, -8), D'(3, -8).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(3, -11), C'(9, -11), C'(9, -8), D'(3, -8). Answer: Translate 13 down.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(-3,5), B'(-9, 5), C'(-9, 8), D'(-3, 8).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(-3,5), B'(-9, 5), C'(-9, 8), D'(-3, 8). Answer: Reflect in the y-axis, then translate 3 units up.

A 10 by 10 Cartesian plane. The original rectangle’s coordinates are: A(3, 2), B(9, 2), C(9, 5), D(3, 5). The transformed rectangle’s coordinates are: A'(5, -6), B'(11, -6), C'(11, -3), D'(5, -3).

Press ‘Answer’ to reveal the coordinates of the transformed image.

A'(5, -6), B'(11, -6), C'(11, -3), D'(5, -3). Answer: Translate 2 right, then 8 down.

What’s that transformation going to look like?

Predicting what a translation, rotation or reflection will look like helps us be sure a transformation is done correctly.

For each of the following choose the best answer.

Consolidation

Transforming playing card symbols

From a deck of playing cards select one of these symbols: ♥, ♦, ♣ or ♠. You will translate, reflect, or rotate one of these shapes on a Cartesian plane.

You can use the Cartesian plane printable document, draw and fill your own Cartesian plane, or create a detailed description for each transformation.

  • Reflect your shape across a line of reflection drawn vertically through -3 on the x-axis
  • Rotate a half turn counterclockwise about the origin (0,0)
  • Translate 3 units to the right and 5 units up
  • Rotate a quarter turn (90°) clockwise using the origin (0,0)

Press the Activity button to access Cartesian plane.

Activity (Open PDF in a new window)

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

I feel...

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

Press ‘Discover More’ to extend your skills.

How would you explain the following concepts to someone? What is most important for them to understand?

  • Rotations
  • Reflections
  • Translations

When you review your notes later, reflect on whether you would select a different description based on the material in this learning activity.

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