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

Aug 7, 2018

$\text{ }$
$A \left(5 , 4\right) , B \left(7 , 9\right) \mathmr{and} C \left(5 , 8\right)$

Bisectors:

$D \left(6 , 8.5\right) \mathmr{and} G \left(7.25 , 6\right)$ with $D G = 2.8 \text{ units}$
$E \left(6 , 6.5\right) \mathmr{and} G \left(7.25 , 6\right)$ with $E G = 1.35 \text{ units}$
$F \left(5 , 6\right) \mathmr{and} G \left(7.25 , 6\right)$ with $F G = 2.25 \text{ units}$

#### Explanation:

$\text{ }$
Triangle $A B C$:

Vertices: $A \left(5 , 4\right) , B \left(7 , 9\right) \mathmr{and} C \left(5 , 8\right)$

Construct a perpendicular bisector:

1. for side $A B$,

find the mid-point: $E \left(6 , 6.5\right)$
$\text{ }$
2. for side $B C$,

find the mid-point: $D \left(6 , 8.5\right)$
$\text{ }$
3. for side $A C$,

find the mid-point: $F \left(5 , 6\right)$

Measure the magnitudes of the perpendicular bisectors:

$E G = 1.35 \text{ Units}$

$F G = 2.25 \text{ Units}$

$D G = 2.8 \text{ units}$

Examine the constructed sketch below and verify:

Hope it helps.