Exploring Reflections 6
Using the line tool again, connect each point on the preimage to their corresponding points on the image (A to A', B to B', C to C') by clicking each set of points. Now select the select tool and move the sliders around slowly. Watch what changes and what stays the same. What is the relationship between the lines connecting the preimage to the image? What is the relationship between the line of reflection and the lines connecting the preimage to the image?
Go ahead and check the answer to the questions on this page and make sure you got the last question correct. Now for the magic. Find the slope of one of the lines connecting the preimage to the image, and without moving the sliders, find the slope of the line of reflection. Now move the sliders at least a bit. Find both slopes again. Move the sliders again, and find both slopes a last time. See if you can figure out the relationship between slopes of perpendicular lines.