# Perpendicular Bisectors - Page 2

Questions

- How do you write the equation of the perpendicular bisector of the segment with the given endpoints #(2,5)# and #(4,9)#?
- A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
- A triangle has corners at #(4 , 1 )#, ( 2, 4 )#, and #( 0, 2 )#. What are the endpoints of the triangle's perpendicular bisectors?
- ABC is a triangle whose sides AB = 6 cm, BC = 8 cm and AC = 12 cms. D is such a point situated on AC that angle ADB = angle ABC. Find the length of BD ?
- How do you find the perpendicular bisectors of a triangle?
- Maya drives from New York City to Boston at a rate of 40 MPH and drives at a rate of 60 MPH on the return trip. What was his average speed for the entire trip? Use the Harmonic mean to compute? Construct the HM geometrically?
- Let #A(x_a,y_a)# and #B(x_b,y_b)# be two points in the plane and let #P(x,y)# be the point that divides #bar(AB)# in the ratio #k :1#, where #k>0#. Show that #x= (x_a+kx_b)/ (1+k)# and #y= (y_a+ky_b)/( 1+k)#?
- A triangle has corners at #(2 , 4 )#, ( 3, 1 )#, and #( 8, 3 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
- In a triangle ABC (figure) the points P and Q are selected in the sides AC and BC respectively in a way that PC is half of BC and QC is half of AC:#bar(PC)/bar(BC) = 1/2; bar(QC)/bar(AC)= 1/2#. Find #bar(PQ)# if the side #bar(Ab)# is 20?
- A line segment is bisected by a line with the equation # 2 y + 9 x = 3 #. If one end of the line segment is at #(3 ,2 )#, where is the other end?
- A line segment is bisected by a line with the equation # - y + 4 x = 3 #. If one end of the line segment is at #( 2 , 6 )#, where is the other end?
- A line segment is bisected by line with the equation # 6 y - 2 x = 1 #. If one end of the line segment is at #(4 ,1 )#, where is the other end?
- In triangle ABC, AB=AC.The circle through B touches the side AC at the mid-point D of AC, passes through a point P on AB. Prove that 4 ×AP = AB ?
- The following set of coordinates (0, 4), (0,7), (1, 5), (1, 2) represents what figure?
- A line segment is bisected by line with the equation # 6 y - 7 x = 3 #. If one end of the line segment is at #(4 ,2 )#, where is the other end?
- Let #P(a,b) and Q(c,d)# be two points in the plane. Find the equation of the line #l# that is the perpendicular bisector of the line segment #bar(PQ)#?
- A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #(7 ,8 )#, where is the other end?
- A line segment is bisected by a line with the equation # - 6 y + 2 x = 3 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
- A line segment is bisected by line with the equation # 3 y - 3 x = 4 #. If one end of the line segment is at #(2 ,4 )#, where is the other end?
- Explain two attributes a parallelogram and a rectangle have in common ?