E1.4 Describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations.
Activity 1: Reflection
A quadrilateral has coordinates A (-5, 3), B (-3, 4), C (2, 5) and D (5, 2). Find the coordinates of the image obtained as a result of a reflection about the x-axis. Describe the effect of this reflection on the coordinates of the image.
Activity 2: Predict and Perform a Rotation, Translation and Dilation
In a Cartesian plane, draw the image of parallelogram ABCD using the following coordinates: A (-5, 2), B (-2, 2), C (-1, 4) and D (-4, 4).
- Before you rotate your figure 180° (½ turn) counterclockwise, predict the results of this transformation. Describe the effect of this rotation on the coordinates of the image.
- Before you translate your figure by (-3, 4), predict the results of this transformation. Describe the effect of this translation on the coordinates of the image.
- Before dilating your figure by a scale factor of 3, predict the results of this transformation. Describe the effect of this dilation on the coordinates of the image.
Source: adapted and translated from En avant, les maths!, 7e année, ML, Sens de l’espace, p. 24.