Parallelogram (Coordinate Geometry)
A quadrilateral with both pairs of opposite sides parallel and congruent, and whose location on the coordinate plane is determined by the coordinates of the four vertices (corners).
Try this Drag any vertex of the parallelogram below. It will remain a parallelogram and its dimensions calculated from its coordinates. You can also drag the origin point at (0,0).
In coordinate geometry, a parallelogram is similar to an ordinary parallelogram (See parallelogram definition ) with the addition that its position on the coordinate plane is known. Each of the four vertices (corners) have known coordinates. From these coordinates, various properties such as its altitude can be found.
It has all the same properties as a familiar parallelogram:
- Opposite sides are parallel and congruent
- The diagonals bisect each other
- Opposite angles are congruent
Sides and diagonals
The lengths of the four sides and two diagonals can be found by using the method described in Distance between two points to find the distance between point pairs.
For example, in the figure above click 'reset' and select "show diagonals' in the options menu. Using the method in Distance between two points, the diagonal AC is the distance between the points A and C:
Diagonal AC
=
√
(
48
−
6
)
2
+
(
26
−
7
)
2
=
46.1
Similarly the side AB can be found using the coordinates of the points A and B:
Side AB
=
√
(
18
−
6
)
2
+
(
26
−
7
)
2
=
22.5
Altitude
The altitude of a parallelogram is the perpendicular distance from a vertex to the opposite side (base). In the figure above select "Show Altitude" in the options menu. It will show the altitude from B to the opposite side AB.
The calculate the length of an altitude, we need to find the perpendicular distance from a point to a line. In the above figure we need the distance from B to the line AD.
No comments:
Post a Comment