Question

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

Answer 1

`" "`
`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:

Hope it helps.