# In a #DeltaXYZ# having #X(-3,2)#, #Y(-5,-6)# and #Z(-5,0)#, is perpendicular bisector of #YZ# same as median from #X#?

##### 2 Answers

The equations are not the same.

#### Explanation:

Find the midpoint of YZ using the midpoint formula

Since YZ is a vertical line:

The **perpendicular bisector** is a horizontal line:

The median from X goes from

Equation of the median

Use either the midpoint or point X to find b:

**Equation of the median:**

Perpendicular bisector of **not** the same line as the median from

#### Explanation:

As the abscissa (i.e.

and as such its perpendicular bisector will be parallel to

As midpoint of

equation of perpendicular bisector is

and median from

or

or

or

Note it is different from the equation of median given in question.

Obviously perpendicular bisector of **not** the same line as the median from