Area Using Coordinates

In geometry, a coordinate system is a system which uses a set of numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in 'the x-coordinate'. In elementary mathematics the coordinates are taken to be real numbers, but in more advanced applications coordinates can be taken to be complex numbers.
(Source: Wikipedia)

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Example problems for area using coordinates

Area using coordinates problem 1:
                      Find the area of the square using the coordinates A (3, 4), B (7, 7), C (4, 7), D (7, 11). Dimension in centimeter.
Solution:
       First we have to find the distance between the two corners. This distance value is equal to side length of the square.
Formula:
Distance (s) = √ ((x₂ – x₁)² + (y₂ – y₁)²)
Distance between A & B is,
Distance (s) = √ ((7 – 3)² + (7 - 3)²)
                       = √ (25)
                       = 5 cm
Side length of the square is (s) = 5 cm
Area of the square = s²
Substitute the given side length value in the above equation, we get
Area = 25cm²
         = 25 cm²
Answer:
The area of square is 25 cm²
Area using coordinates problem 2:
                  Find the area of the square using the coordinates A (12, 5), B (6, - 3), C (5, 10), D (11, 2). Dimension in centimeter.
Solution:
       First we have to find the distance between the two corners. This distance value is equal to side length of the square.
Formula:
Distance (s) = √ ((x₂ – x₁)² + (y₂ – y₁)²)
Distance between A & B is,
Distance (s) = √ ((6 – 12)² + (- 3 - 5)²)
                       = √ (100)
                       = 10 cm
Side length of the square is (s) = 10 cm
Area of the square = s²
Substitute the given side length value in the above equation, we get
Area = 100 cm²
        = 100 cm²
Answer:
The area of the square is 100 cm²

Area using coordinates problem 3:
Find the area of the square using the coordinates A (10, 2), B (- 5, 2), C (6, 5), D (18, - 4). Dimension in centimeter.
Solution:
First we have to find the distance between the two corners. This distance value is equal to side length of the square.
Formula:
Distance (s) = √ ((x₂ – x₁)² + (y₂ – y₁)²)
Distance between A & B is,
Distance (s) = √ ((- 5 – 10)² + (2 - 2)²)
                       = √ (225)
                       = 15 cm
Side length of the square is (s) = 15 cm
Area of the square = s²
Substitute the given side length value in the above equation, we get
Area = 15² cm²
        = 225 cm²
Answer:
The area of the square is 225 cm²

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Practice problems for area using coordinates

Find the area of the square using the coordinates A (- 5, - 6), B (2, - 3), C (9, -1), D (2, 2). Dimension in centimeter.
Answer:
The final answer is 58 cm²

Area using coordinates problem 2:
Find the area of the square using the coordinates A (3, 7), B (6, - 2), C (9, 2), D (0, 5). Dimension in centimeter.
Answer:

The final answer is 90 cm²