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Worksheet: Finding the Distance between Two Points on a Coordinate Plane Using the Pythagorean Theorem

Q1:

Consider the two points and .

Using the Pythagorean theorem, find an expression for the length of .

  • A
  • B
  • C
  • D
  • E

Using the distance formula, find the distance between the points and Give your answer as a surd in its simplest form.

  • A6
  • B8
  • C
  • D2
  • E

Q2:

What is the distance between the point and the origin?

  • A length units
  • B length units
  • C length units
  • D length units

Q3:

Find the distance between the point and the point of origin.

  • A length units
  • B length units
  • C length units
  • D length units

Q4:

Find the distance between the points and .

  • A16 length units
  • B length units
  • C length units
  • D4 length units
  • E length units

Q5:

Find the distance between the points and .

  • A21 length units
  • B length units
  • C length units
  • D length units
  • E length units

Q6:

Find the distance between the points and .

  • A13 length units
  • B length units
  • C length units
  • D length units
  • E3 length units

Q7:

Find the distance between the points and .

  • A14 length units
  • B length units
  • C length units
  • D length units
  • E length units

Q8:

The distance between and is 5. What are the possible values of ?

  • A or
  • B or 4
  • C or
  • D or 4

Q9:

If and , where length units, find all the possible values of .

  • A or
  • B or
  • C or
  • D or

Q10:

If the distance between the two points and is 9, find all possible values of .

  • A or
  • B or
  • C or
  • D or
  • E or

Q11:

If the distance between the two points and is 5, find all possible values of .

  • A or
  • B or
  • C or
  • D or
  • E or

Q12:

If the distance between the two points and is 10, find all possible values of .

  • A or
  • B or
  • C or
  • D or
  • E or

Q13:

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

  • A
  • B
  • C
  • D

Q14:

Given , , and , what is the perimeter of ?

  • A
  • B
  • C18
  • D

Q15:

How far is the butcher from the garage?

Q16:

Two baseball posts were positioned at and . Find the distance between the posts giving the answer to one decimal place.

Q17:

Gerald is making a map of his local area measured in yards. The coffee shop is at and the Italian restaurant is at . Find the distance between the coffee shop and the Italian restaurant giving the answer to one decimal place.

Q18:

Three radio towers are located at , , and . Determine the location of a fourth radio tower that is equidistant from the other three towers.

  • A
  • B
  • C
  • D
  • E

Q19:

The point is located on the line segment between point and point . Given that the distance from to is twice the distance from to , find the coordinates of point .

  • A
  • B
  • C
  • D
  • E

Q20:

A small craft in Lake Ontario sends out a distress signal from the coordinates . One rescue boat is at the coordinates , while a Coast Guard boat one is at the coordinates . Assuming both boat travel at the same rate, which one will get to the distressed boat first?

  • AThe coast guard craft
  • BThe rescue boat

Q21:

On a map, coordinates are expressed in miles. The coordinates for San Francisco are and those for Sacramento are . Find the distance between the cities to the nearest mile.

Q22:

On a map where the coordinates represent miles from a fixed point, San Jose’s is at and San Francisco's at . Find the distance between San Jose and San Francisco to the nearest mile.

Q23:

Points and have coordinates and respectively. Point lies on such that and are in the ratio of .

Write the quotient of the length of by the length of in terms of and .

  • A
  • B
  • C
  • D
  • E

Find an expression for the difference between the coordinates of and .

  • A
  • B
  • C
  • D
  • E

Find an expression for the difference between the coordinates of and .

  • A
  • B
  • C
  • D
  • E

Find an expression for the coordinates of .

  • A
  • B
  • C
  • D
  • E