As noted above, to measure distances correctly, the ruler needs to be positioned so that it joins the point on the line that’s being reflected to the centre of the circle, with the 0 at the point on the line.
Students will need to measure, to the nearest mm, distances from several points on the line to the circle, and mark the reflections of each point. Students can try this activity for themselves with just a pencil, ruler, compasses, and plain paper. To focus on what’s happening, you can hide the line by unticking the “Show line box” and ticking the “Show the perpendicular” box.Now slowly drag the blue point up and down the line to form the reflection. Tick the “Show and mark reflection” box.Once you’ve decided where you’d like the line, do not move it again. Use the grey tool to move the line horizontally, keeping it to the left of the semicircle.This only works because GCSE transformations always map straight lines to straight lines.) Suggested activity Procedurally, they may only be doing that, but this is a shortcut that leads to them transforming all points once the vertices are joined together using straight line segments. (Students sometimes think that they only transform vertices. This helps reinforce an idea common to all transformations: when you transform an object, you transform all points on that object. Instead, you have to pick and reflect lots of points to get a good sense of what the image will look like. Secondly, because of the curved mirror, it is not possible to simply pick two points to reflect and then to join them up with a straight line. To find the perpendicular distance from a point to a circle, simply position your ruler so that it joins the point of interest to the centre of the circle. It is nevertheless a fun thing to try, and this activity highlights an important idea about reflection and an important idea about all transformations.įirstly, this helps draw attention to perpendicular distances. Reflection in a curve does not come up at GCSE.
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