POLYGONS IN THE COORDINATE PLANE WORKSHEET

Problem 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.

Problem 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 ?

2. Answer :

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.

Problem 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.

Problem 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.

Problem 5 :

The vertices of a rectangle are J(2, 7), K(4, 7), L(4, 15) and M(2, 15). Find the perimeter and area of the shape.

Solution :

Length of the rectangle = 2 units 

Width of the rectangle = 15 - 7 ==> 8 units

Perimeter of rectangle = 2(length + width)

= 2(2 + 8)

= 2(10)

= 20 units

Area of rectangle = length x width

= 2 x 8

= 16 square units

Problem 5 :

The vertices of a polygon are L(1, 2), M(1, 6), N(7, 6), O(7, 2), P(5, 0), and Q(3, 0). Graph the polygon. Then find its area. A = _____ square units.

Solution :

Area of the shape = area of rectangle + area of trapezium

Dimensions of rectangle :

Length = 7 - 1 ==> 6 units

Width = 6 - 2 ==> 4 units

Dimensions of trapezoid :

Parallel sides

a = 7 - 1 ==> 6 units 

b = 5 - 3 ==> 2 units

height = 2 - 0 ==> 2 units

Area of the shape = 6 x 4 + (1/2) x 2 x (6 + 2)

= 24 + 8

= 32 square units.

Problem 6 :

A gardener uses a coordinate grid to design a new garden. The gardener uses polygon WXYZ on the grid to represent the garden. The vertices of this polygon are W(3, 3), X(−3, 3), Y(−3, −3), and Z(3, −3). Each grid unit represents one yard.

1. Graph the points, and connect them in order. What is the shape of the garden?

2. How much fencing will the gardener need to enclose the garden? Each side of the garden is The gardener will need the garden. yards in length. yards of fencing to enclose

3. What is the area of the garden?

Solution :

1.

Since length and width are the same, it must be a square.

2. Length of fencing = 4 x side length

= 4 x 6

= 24 units.

3. Area of the garden = 6 x 6

= 36 square units.

Problem 7 :

A clothing designer makes letters for varsity jackets by graphing the letters as polygons on a coordinate plane. One of the letters is polygon ABCDEF. The vertices of this polygon are A(3, −2), B(3, −4), C(−3, −4), D(−3, 4), E(−1, 4), and F(−1, −2). Each grid unit represents one inch. Graph the points on the coordinate plane, and connect them in order. Identify the letter formed. Then find its area.

Solution :

By drawing a horizontal line through F, we separate the shape into two rectangles.

Area of rectangle below = 6 x 2

= 12 square units

Area of the rectangle vertically = 6 x 2

= 12 square units

Total area = 12 + 12

= 24 square units

Problem 8 :

What is the word for the horizontal line at the bottom of the coordinate plane ?

a) Ordered pair    b)  x-axis   c) y-axis    d)  Origin

Solution :

The horizontal line is x-axis.

Problem 9 :

What is ordinate R ?

a)  (0, 1)   b)  (1, 0)     c)  (2, 5)    d)  (2, 3)

Solution :

The ordered pair represented by the point R is (0, 1). So, option a is correct.

Problem 10 :

Give coordinates for the vertices of a triangle that could have an area of 35 square units. Prove that your triangle fits the description by finding its area.

Solution :

Area of triangle = 35 square units

(1/2) x base x height = 35

base x height = 35(2)

= 70 square units.

base = 7 and height = 10

In this way we may create the triangle with this measures.

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