You just tried one way of transforming an object by reflecting it and then sliding it. Multiple transformations can get a little harder to do on plain paper. In many cases, mapping the points of the original figure to the transformed one can be more accurate. You can use graph paper to do your mapping. By using graphing paper, you can see what happens to the points.
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Let's look at two types of compound transformations. In the first problem, we must reflect the image about the x-axis, then translate it two units to the right. Follow the steps I complete and do the same on your own. First, in the original image, place a black dot on the upper right corner of the red shape. It can be anywhere, but because the shape is not symmetric, this location will be easier to visualize. For the first transformation, which is the reflection about the x-axis, the coordinates of the black dot on the red shape are (-2, 6). The reflection across the x-axis is a vertical reflection from above the x-axis to below the x-axis, so the black dot will become (-2, -6). Once the point is found, you can construct the shape from there by creating a shape that mirrors the original red shape (in blue). For the last transformation, the blue shape needs to move 8 units to the right and then 2 units down to form the final image (in green).
For the second problem, we must dilate the image by a factor of two, and then rotate it 90 degrees counter-clockwise. First we will complete the dilation. For this it is important obtain the coordinates of each vertex. One vertex is at (2,1), another is at (4, 2), and the last is at (4, 4). When dilating, we multiply each value of every coordinate by the scale factor. In this case, the point at (2,1) dilates to (4,2)… the point at (4,2) dilates to (8,4)… and the point at (4,4) dilates to (8,8). Now, to rotate the blue triangle 90 degrees clockwise, we can use a shortcut. Rather than drawing 90 degree angles that meet at the origin, or counting steps, you might have recognized that this type of rotation can be completed by first switching the x- and y-coordinates. Then, change the sign of the new x coordinate. For example, the point (4,2) becomes (-2,4), the point (8,4) becomes (-4,8), and the point (8,8) becomes (-8,8). A similar rule can be found for rotations clockwise 90 degrees or even rotations of 180 degrees.
Please be sure to review the techniques shown in this video until you are comfortable enough to complete them on your own. Practice them by making up problems like them on your own. Good Luck!
Question
Why is using a point on a figure or shape helpful when building multiple transformations?
