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.

This lesson includes 50 additional questions and 306 additional question variations for subscribers.

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