Lesson Worksheet: Distance on the Coordinate Plane: Pythagorean Formula Mathematics • 8th Grade

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


Find the distance between the point (2,4) and the point of origin.

  • A22 length units
  • B32 length units
  • C25 length units
  • D6 length units


Find the distance between the points 𝐴 and 𝐵.

  • A4 length units
  • B16 length units
  • C58 length units
  • D213 length units
  • E10 length units


Which of the following points is at a distance of 52 from the origin?

  • A52,52
  • B(5,5)
  • C(0,5)
  • D(5,0)


The coordinates of the points 𝐴, 𝐵, and 𝐶 are (𝐾,2), (2,8), and (9,6) respectively. Given that 𝐴𝐵=𝐵𝐶, find all possible values of 𝐾.

  • A𝐾=3 or 𝐾=7
  • B𝐾=3 or 𝐾=7
  • C𝐾=3 or 𝐾=7
  • D𝐾=3 or 𝐾=7


The distance between (𝑎,5) and (1,1) is 5. What are the possible values of 𝑎?

  • A𝑎=2 or 4
  • B𝑎=2 or 4
  • C𝑎=2 or 4
  • D𝑎=2 or 4


If 𝐴(7,𝑥) and 𝐵(9,14), where 𝐴𝐵=417length units, find all the possible values of 𝑥.

  • A𝑥=10 or 𝑥=18
  • B𝑥=10 or 𝑥=18
  • C𝑥=10 or 𝑥=18
  • D𝑥=10 or 𝑥=18


What is the kind of triangle that the points 𝐴(2,7), 𝐵(1,6), and 𝐶(9,6) form with respect to its sides?

  • AScalene triangle
  • BEquilateral triangle
  • CIsosceles triangle


Point (6,7) is on the circle with center (7,1). Decide whether point (8,9) is on, inside, or outside the circle.

  • AOutside the circle
  • BInside the circle
  • COn the circle


Given 𝐴(4,5), 𝐵(5,5), and 𝐶(4,7), what is the perimeter of 𝐴𝐵𝐶?

  • A16+210
  • B16+25
  • C16+413
  • D18


James is making a map of his local area measured in meters. The coffee shop is at (5,4) and the Italian restaurant is at (0,6). Find the distance between the coffee shop and the Italian restaurant giving the answer to one decimal place.

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