A polygon is a closed plane figure formed by three or more line segments that meet only at their endpoints. A vertex is the point where two sides of a polygon meet. The vertices of a polygon can be represented as ordered pairs, and the polygon can then be drawn in the coordinate plane.
Example 1 :
Sheila wants to make a pattern of a tile shape with the points A(3, 5), B(4, 6), C(5, 5) and D(4, 4).
What polygon will she get ?
Solution :
Step 1 :
Let us plot the points A(3, 5), B(4, 6), C(5, 5) and D(4, 4) on the coordinate plane.
Step 2 :
Connect the points in order.
Step 3 :
The polygon formed is a square.
Example 2 :
David wants to make a pattern of a tile shape with the points P(-5, 2), Q(-4, 3), R(0, 3), S(1, 2), T(1, -2), U(0, -3), V(-4, -3) and W(-5, -2).
What polygon will he get ?
Solution :
Step 1 :
Let us plot the points P(-5, 2), Q(-4, 3), R(0, 3), S(1, 2),T(1, -2), U(0, -3), V(-4, -3) and W(-5, -2) on the coordinate plane.
Step 2 :
Connect the points in order.
Step 3 :
The polygon formed is an octagon.
Example 3 :
John wants to make a pattern of a tile shape with the points A(-4, 2), B(2, 2), C(2, -2) and D(-4, -2)
What polygon will he get ?
Solution :
Step 1 :
Let us plot the points A(-4, 2), B(2, 2), C(2, -2) and D(-4, -2) on the coordinate plane.
Step 2 :
Connect the points in order.
Step 3 :
The polygon formed is a rectangle.
Example 4 :
How is the number of vertices related to the number of sides of the polygon and to the type of polygon ? Give two examples.
Solution :
They are the same.
That is, if a polygon has 3 vertices, it would have 3 sides.
Example :
A polygon with 3 vertices is a triangle and a polygon with 6 vertices is a hexagon.
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