In class today, I passed back a number of tests which I graded over the weekend and were on the progress reports yesterday. We also studied properties of reflections and perpendicular bisectors. Students took notes on how to find the equation of a perpendicular bisector line between any two points. This relates to reflections (the reflection line is a perpendicular bisector between any point and its reflection) and the perpendicular bisector can also be used to find the center of rotation.
Question: How would you find the equation of the perpendicular bisector line for the points A(4, 2) and B(2, 7)?
Answer: First find the slope between these two points , now note that the slope of a line perpendicular must be the negative reciprocal slope, so our perpendicular bisector will have slope .
Now, we need to find the midpoint of A and B – so we find the average of their x and y- coordinates:
Ok, so we know the slope of the perpendicular bisector and one of the points on the line, we can use point-slope form to write the equation of the line in the form y = m(x – x1) + y1
If we want this equation in slope-intercept (y = mx + b) form, we just need to simplify the equation above.
(distribute the 2/5)
(simplify 2/5 times -3)
(common denominators for like terms)