**Polygons in the Coordinate Plane :**

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.

**Examples :**

A polygon with 3 vertices is a triangle and a polygon with 6 vertices is a hexagon.

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