A triangle has corners at #(5 , 4 )#, ( 7 , 9)#, and #( 5 , 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?

1 Answer
Aug 7, 2018

#" "#
#A(5,4), B(7,9) and C(5,8)#

Bisectors:

#D(6,8.5) and G(7.25,6)# with #DG=2.8 " units"#
#E(6,6.5) and G(7.25,6)# with #EG=1.35 " units"#
#F(5,6) and G(7.25,6)# with #FG=2.25 " units"#

Explanation:

#" "#
Triangle #ABC#:

Vertices: #A(5,4), B(7,9) and C(5,8)#

Construct a perpendicular bisector:

  1. for side #AB#,

    find the mid-point: #E(6,6.5)#
    #" "#
    2. for side #BC#,

    find the mid-point: #D(6,8.5)#
    #" "#
    3. for side #AC#,

    find the mid-point: #F(5,6)#

Measure the magnitudes of the perpendicular bisectors:

#EG=1.35" Units"#

#FG=2.25" Units"#

#DG=2.8" units"#

Examine the constructed sketch below and verify:

enter image source here

Hope it helps.