If there is no coordinate plane for my transformations I would know that they are accurate because of the series of tests I would preform on each transformation. For my translation, which is my first transformation, I would make sure that it is translated along a vector, and that the figure got translated the same distance, and in the same direction as the vector. My second transformation is a rotation and for this I would make sure that each point on the figure is keeping the same distance from the center of rotation that which its pre-image had. Also, I would measure from the center of rotation to each point, making sure that the angle of rotation is all the same. Last but not least, I have a reflection for my transformation. For this, I would have to make sure that each point on the pre-image and image is equidistant from the line of reflection. Also, I would have to make sure that the line forms a [math]90^\circ[/math]angle with any line segment connecting a certain point on the pre-image to the image.