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

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

Q1:

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

  • A2√2 length units
  • B3√2 length units
  • C2√5 length units
  • D√6 length units

Q2:

Find the distance between the points 𝐴 and 𝐵.

  • A4 length units
  • B16 length units
  • C√58 length units
  • D2√13 length units
  • E√10 length units

Q3:

Which of the following points is at a distance of 5√2 from the origin?

  • A5√2,5√2
  • B(5,5)
  • C(0,5)
  • D(5,0)

Q4:

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

Q5:

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

Q6:

If 𝐴(−7,𝑥) and 𝐵(9,14), where 𝐴𝐵=4√17length 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

Q7:

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

Q8:

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

Q9:

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

  • A16+2√10
  • B16+2√5
  • C16+4√13
  • D18

Q10:

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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