a picture of these three.
(a) Circumcentre : Draw perpendicular bisectors of the three
sides. The point where they meet is the Circumcentre. (b)
Orthocentre : Draw the perpendiculars from the third vertex for
each of the three sides. The point where they meet is the
Orthocentre. (c) Incentre : Draw angle bisectors for each of the
three angles. The point where they meet is the Incentre.
Why do perpendicular bisectors of the three sides of
a triangle all meet at a single point? and also why
do angle bisectors of the three sides of a triangle all
meet at a single point ?
Prove the following theorem:
In a Pasch geometry, a quadrilateral is a convex quadrilateral
if and only if the vertex of each angle is contained in the
interior of the opposite angle.
(Area of a convex polygon)
A polygon is convex if it contains any line segment that connects
two points of the polygon. Write a program that prompts the user to
enter the number of points in a convex polygon, then enter the
points clockwise, and display the area of the polygon.
Sample Run
Enter the number of points: 7
Enter the coordinates of the points:
-12 0 -8.5 10 0 11.4 5.5 7.8 6 -5.5 0 -7 -3.5 -5.5
The...
Match the words with the correct
definition.
Perpendicular
Parallel
Colinear
Fix
Horizontal
Definitions
Defines a location and size for an entity.
Aligns two entities.
Defines two entities as 90 degree apart.
Defines a line in the X direction.
Defines an entity equidistant from another entity.
A convex polygon is defined as a polygon where all its internal
angles are less than 180 degrees and no edges cross each other. You
can assume the vertex with the smallest x-coordinate (assuming
origin at bottom left) is the first coordinate and other vertices
are numbered in a counter-clockwise direction. Figure 1 shows an
example of such a polygon where V[1] is the first polygon. For
simplicity, you can also assume all polygon vertices have distinct
x and y...
every quadrilateral tessellates the plane. However, can an
arbitrary quadrilateral such as the one shown below have all its
sides altered and still tessellate the plane? Decide which methods
described in this activity set you can use to alter the sides of
this quadrilateral and tessellate the plane. In the pictured
quadrilateral, no sides are of equal length and no sides are
parallel. For each method you use, make a template for your figure,
and determine whether or not it...
Write an inheritance hierarchy
for classes
Quadrilateral,
Trapezoid,
Parallelogram, Rectangle
and Square.
Use Quadrilateral as the
superclass of the hierarchy. Create and use a Point class to
represent the points in each shape. Make the hierarchy as deep (
i.e., as many levels ) as possible. Specify the instance variables
and methods for each class. The
private instances variables
of Quadrilateral should
be the x-y coordinate
pairs for the four endpoints of the
Quadrilateral. Write a program
that instantiates objects...