Minds On
Let’s review transformations
Examine the following image on a Cartesian plane.
Then, identify the transformation (e.g., 180° clockwise rotation) that was used to move the object from its original position.
Action
Activity one: follow the triangle
Using a virtual tool, pencil and paper, Cartesian plane manipulative, or by recording a detailed description, please construct the following triangle:
A(3, 2), B(6, 5) and C(5, 2).
Using this triangle, perform the following transformations and record the new coordinates on a table beside the new shape:
- Reflect the triangle over the Y axis. Label the reflected image A′B′C′. Using this new triangle, use the X axis as a line of reflection. Draw the new triangle, label it A″, B″, C″ and record the coordinates.
- On a new Cartesian plane, draw the third triangle based on your coordinates. Label it DEF. Rotate the triangle 180 degrees around the origin (where the x-axis intersects the y-axis). Record the new coordinates. What do you notice?
- Finally, using those new coordinates, translate your triangle 4 units to the right and 7 units down. To do this, move each coordinate: D′, E′, and F′, 4 units to the right and 7 units down. Label the new image D″, E″, F″.
To reveal the solutions for each of the three tasks, press on each ‘Task’ tab that follows next.
This image shows a 4-quadrant C artesian plane with an obtuse triangle in quadrant I, II and III. The coordinates are A (3,2), B (6,5), C (5,2); A’(-3, 2), B’(-6,5) C’ (-5,2); A’’(-3,-2), B’’(-6,-5), C’’(-5,-2).
After rotating the triangle 180°, the coordinates of D′E′F′ are D′(3,2), E′(6,5), F′(5,2).
I noticed that the triangle is back in the original position after the rotation. I think this might mean that it is a reflection across the y-axis and a reflection across the x-axis.
This image shows a 4-quadrant Cartesian plane with an obtuse triangle in quadrant I, and III. The coordinates are D(-3,-2), E(-6,-5), F(-5,-2). D’(3,2), E’(6,5), F’ (5,2);
This image shows a 4-quadrant Cartesian plane with an obtuse triangle in quadrant I, and IV. The coordinates are D’(3,2), E’(6,5), F’ (5,2); D’’(7,-5), E’’(10, -2), F’’(9,-5)
Activity two: predict coordinates
Construct the following triangle:
A (-10, -3), B (-8, -3), C (-9, -5)
Press ‘Triangle’ to reveal the location of the triangle.
Image shows a 4-quadrant Cartesian plane with an isosceles triangle in quadrant 3. It’s coordinates are A(-10, -3), B(-8, -3), C(-9, -5).
Using this triangle, predict the coordinates of the new location of the shape based on the transformations below.
Record your predictions using a method of your choice.
1. Predict the coordinates of the triangle after a reflection over the X axis.
Press ‘Answer’ to reveal the solution to the first task.
My original triangle is in Quadrant III. After a reflection over the x-axis, it would be in Quadrant II. I predict that the x coordinates won’t change but the y coordinates will become positive.
After a reflection over x-axis, the coordinates will be: A (-10, 3), B (-8, 3), C (-9, 5)
2. Using the coordinates of this new triangle, predict the location of the triangle after a reflection over the Y axis.
Press ‘Answer’ to reveal the solution to the second task.
My triangle is now in Quadrant II. I predict that after reflecting it over the y-axis, my triangle will be in Quadrant I so the x coordinate will become positive, and the y coordinate will stay the same.
After a reflection over Y axis, the coordinates will be A (10, 3), B (8, 3), C (9, 5)
3. Using the original coordinates of the triangle, predict the coordinates of the triangle after a 90° counterclockwise rotation around the origin.
Press ‘Answer’ to reveal the solution to the third task.
My original triangle was in Quadrant III. If I rotate it 90° CCW around the origin, it will end up in Quadrant IV. The values for X and Y exchange positions but some signs change. The original Y coordinates change sign as they now become the new X coordinates. The original X coordinates keep their original sign as they now become the Y coordinates.
After a 90° counterclockwise rotation around the origin, the coordinates will be: A (3, -10), B (3, -8), C (5, -9).
4. Using the original coordinates of the triangle, predict the new coordinates of the triangle after a translation of 4 units to the right and 2 units down.
Hint: To do this, move each coordinate: A, B, and C, 4 units to the right and 7 units down.
Press ‘Answer’ to reveal the solution to the fourth task.
My original triangle was in Quadrant III. If I translate it 4 to the right and 7 down, it will remain in Quadrant III.
After a translation of 4 units to the right and 2 units down, the coordinates will be: A (-6, -10), B (-4, -10), C (-5, -12).
Consolidation
Reflect and represent
Reflect on your learning in this activity.
Consider the following:
- What strategies did you use to make your transformations (e.g., how do you make a rotation?)
- What steps did you take to make these transformations?
- How do you know if your transformation is accurate?
Create a drawing, written note or audio note outlining what you know about transformations.
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.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.
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