# Perpendicular Bisectors - Page 4

Questions

- A line segment is bisected by a line with the equation # - 2 y + 3 x = 1 #. If one end of the line segment is at #(6 ,3 )#, where is the other end?
- In the plane of the triangle #ABC# we have #P# and #Q# such that #vec(PC)=3/2vec(BC)#and #vec(AQ)=1/4vec(AC)#,and #C'#is the middle of #[AB]#.How to demonstrate that #P,Q # and #C'# are collinear points with theorem of Menelaus?
- In the figure below, find #bar(AE)# if #bar(AC)# is a perpendicular bisector of #bar(DE)#?
- A line segment is bisected by a line with the equation # 2 y -4 x = 1 #. If one end of the line segment is at #(3 ,8 )#, where is the other end?
- A triangle has vertices at #A(a,b )#, #C(c,d)#, and #O(0,0)#. What are the endpoints and length of the perpendicular bisector of AC ?
- A line segment is bisected by a line with the equation # 4 y + 3 x = 8 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
- A line segment is bisected by a line with the equation # - 5 y + 2 x = 1 #. If one end of the line segment is at #(6 ,4 )#, where is the other end?
- Given 2 numbers #(a,b)# it is possible to perform geometrically the following algebraic operations: a+b, a−b, a*b, a/b. Use only a straight edge and compass to show each operation?
- A line segment is bisected by a line with the equation # - y + 7 x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
- A line segment is bisected by a line with the equation # -3 y + 7 x = 1 #. If one end of the line segment is at #(9 ,2 )#, where is the other end?
- Let #P(x_1, y_1)# be a point and let #l# be the line with equation #ax+ by +c =0#. Show the distance #d# from #P->l# is given by: #d =(ax_1+ by_1 + c)/sqrt( a^2 +b^2)#? Find the distance #d# of the point P(6,7) from the line l with equation 3x +4y =11?
- A line segment is bisected by a line with the equation # - y + 3 x = 1 #. If one end of the line segment is at #(6 ,3 )#, where is the other end?
- In a #DeltaXYZ# having #X(-3,2)#, #Y(-5,-6)# and #Z(-5,0)#, is perpendicular bisector of #YZ# same as median from #X#?
- Constructing the angle 75°?
- A triangle has corners at #(2 , 5 )#, ( 1, 3 )#, and #( 8, 1 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
- A line segment is bisected by a line with the equation # 4 y + 3 x = 4 #. If one end of the line segment is at #( 8 , 9 )#, where is the other end?
- How do you find the equation that is the perpendicular bisector of the line segment with endpoints #(-2, 4)# and #(6, 8)#?
- A line segment is bisected by a line with the equation # - 6 y + 2 x = 4 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
- A line segment is bisected by a line with the equation # 7 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 # - 2 y - x = 2 #. If one end of the line segment is at #( 8 , 7 )#, where is the other end?