# Perpendicular Bisectors

In the realm of geometry, Perpendicular Bisectors emerge as fundamental constructs with profound implications. These geometric entities hold the power to dissect a segment precisely, not only by dividing it into two equal halves but also by introducing the concept of orthogonality. The study of Perpendicular Bisectors extends beyond the mere understanding of geometric shapes, unlocking avenues to explore symmetry, equidistance, and the intricacies of perpendicularity. As we delve into the intricacies of Perpendicular Bisectors, we embark on a journey that unveils their significance in shaping the foundation of geometric principles and applications.

Questions

- How do I find the equation of a perpendicular bisector of a line segment with the endpoints #(-2, -4)# and #(6, 4)#?
- A line segment is bisected by a line with the equation # 4 y + x = 3 #. If one end of the line segment is at #(5 ,6 )#, where is the other end?
- A line segment is bisected by a line with the equation # - 3 y + 2 x = 2 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
- What is an example of a real world situation that implies the perpendicular bisector theorem?
- A line segment is bisected by a line with the equation # 3 y - 8 x = 2 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
- A line segment is bisected by line with the equation # 3 y - 3 x = 1 #. If one end of the line segment is at #(2 ,5 )#, where is the other end?
- A line segment is bisected by a line with the equation # - 2 y - x = 1 #. If one end of the line segment is at #( 8 , 3 )#, where is the other end?
- A line segment is bisected by a line with the equation # -7 y + x = 3 #. If one end of the line segment is at #(1 ,6 )#, where is the other end?
- How to do this perpendicular bisector of a chord question?
- A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?
- A line segment is bisected by a line with the equation # - 3 y + 5 x = 8 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
- A line segment is bisected by a line with the equation # - y + 7 x = 1 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
- Using a compass and straight edge only mark two points A and B. Draw the line #l# through them and find another point C on #l# such that AB = BC?
- A triangle has corners at #(5 , 4 )#, ( 7 , 9)#, and #( 5 , 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
- In a #DeltaABC#, right angled at #A#, a point #D# is on side #AB#. Prove that #CD^2=BC^2+BD^2#?
- A line segment is bisected by a line with the equation # - 3 y + 6 x = 5 #. If one end of the line segment is at #( 3 , 3 )#, where is the other end?
- What is the equation of the perpendicular bisector of a chord of a circle?
- A line segment is bisected by a line with the equation # -3 y + x = 1 #. If one end of the line segment is at #(1 ,6 )#, where is the other end?
- A line segment is bisected by a line with the equation # 7 y + x = 7 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
- How do you find the perpendicular bisector of a line segment?