A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation. When a figure is transformed by a similarity transformation, an image is created that is similar to the original figure. In other words, two figures are similar if a similarity transformation will carry the first figure to the second figure.
The slope of the red line would be 5 as well as long as the lines are parallel. If it were perpendicular, or made an x, then the slope would be (1/5)<span />