Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5). indicate the equation of the line through (2, -4) and having slope of 3/5.

Given endpoint are (4,1) and (2, -5).

For any two points and    

Slope of the line is given by:

Slope(m) =

Slope of the segment for the given end points are:

Now, to find the midpoint of line segment.

Midpoint is halfway between the two end points.

then its y value is halfway between the two y values and Its x value is halfway between the two x values.

i.e,

Midpoint =

Midpoint of the given line segment is;

we have to find the equation of line that is perpendicular bisector of the line segment.

Slope for the perpendicular bisector ;

⇒

Point slope form: An equation of a straight line in the form where m is the slope of the line and are the coordinates of a given points on the line

Using point  slope form to find the equation of line that is the perpendicular bisector;

Using distributive property;

or

or

Therefore, the equation of line that is perpendicular bisector of the segment with given end points is;  

To indicate the equation of line through (2, -4) and having slope of

Using Point slope form definition :

then;

or

Using distributive property:

Subtract 4 from both sides we get;

or

therefore, the equation of line is ,

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