Answer:
1) The slope of the line segment AB is
.
2) The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB is
.
4) The slope of a line perpendicular to line segment AB is
.
Step-by-step explanation:
1) Let
and
. From Analytical Geometry, we get that slope of AB (
), dimensionless, is determined by the following formula:
(1)
If we know that
,
,
and
, the slope of the line segment is:


The slope of the line segment AB is
.
2) The length of the line segment AB (
), dimensionless, can be calculated by the Pythagorean Theorem:
(2)
If we know that
,
,
and
, the length of the line segment AB is:


The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB are, respectively:
(3)
(4)
If we know that
,
,
and
, the coordinates of the midpoint of the line segment AB are, respectively:




The coordinates of the midpoint of the line segment AB is
.
4) From Analytical Geometry we can determine the slope of a line perpendicular to line segment AB as a function of the slope of the line segment:
(5)
If we know that
, then the slope of a line perpendicular to AB is:


The slope of a line perpendicular to line segment AB is
.