Lesson Worksheet: Distance on the Coordinate Plane Mathematics

In this worksheet, we will practice representing rational numbers on the coordinate plane, finding the distance between two points using the Pythagorean theorem, and finding the midpoint.


Use the graph below to determine the points 𝐴, 𝐵, 𝐶, and 𝐷, and find the area of the shape that results from connecting them.

  • A𝐴(4,6), 𝐵(4,6), 𝐶(4,6), 𝐷(4,6), 48
  • B𝐵(4,6), 𝐶(4,6), 𝐴(4,6), 𝐷(4,6), 96
  • C𝐵(4,6), 𝐶(4,6), 𝐴(4,6), 𝐷(4,6), 48
  • D𝐴(4,6), 𝐵(4,6), 𝐶(4,6), 𝐷(4,6), 96


Find the length of the base of Triangle B.


Write the ordered pair for the location of the monkeys.

  • A(3,2)
  • B(4,7)
  • C(4,5)
  • D(6,4)
  • E(3,1)


Find the length of 𝐴𝐵.


Find the lengths of 𝐴𝐵 and 𝐷𝐶, where the coordinates of points 𝐴, 𝐵, 𝐶, and 𝐷 are (2,3), (5,3), (2,4), and (2,5), respectively, considering that a length unit is equal to 1 cm.

  • A𝐴𝐵=5cm, 𝐷𝐶=2cm
  • B𝐴𝐵=2cm, 𝐷𝐶=3cm
  • C𝐴𝐵=7cm, 𝐷𝐶=9cm
  • D𝐴𝐵=7cm, 𝐷𝐶=1cm


Given points 𝐶(16,20) and 𝐷(16,10), calculate the distance between the two points, 𝐶 and 𝐷, considering that a length unit =1cm.


If 𝐴𝐵𝐶𝐷 is a square, where 𝐴(7,2), 𝐵(𝑥,𝑦), 𝐶(4,5), and 𝐷(4,2), find the ordered pair (𝑥,𝑦) that represents 𝐵 and then determine the area of the square considering a unit length =1cm.

  • A𝐵(7,5), area =9cm
  • B𝐵(5,7), area =3cm
  • C𝐵(7,5), area =12cm
  • D𝐵(5,7), area =6cm


Use the graph below to determine the coordinates of the points 𝐴, 𝐵, and 𝐶, then find the area of the resulting figure from connecting the points.

  • A𝐶(2,0), 𝐵(2,5), 𝐴(2,5), 20 area units
  • B𝐴(2,0), 𝐵(2,5), 𝐶(2,5), 20 area units
  • C𝐴(2,0), 𝐵(2,5), 𝐶(2,5), 10 area units
  • D𝐵(2,0), 𝐶(2,5), 𝐴(2,5), 10 area units


Given that one length unit equals 1 cm, find the perimeter of 𝐿𝑀𝑁𝐻, where the coordinates of points 𝐿, 𝑀, 𝑁, and 𝐻 are (7,3), (2,3), (2,9), and (7,9), respectively.


What is the distance between the points (8,2) and (4,2)?

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