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

This worksheet will help you practice finding the distance between two points on the coordinate plane using the Pythagorean theorem. The student is given the coordinates of two points or a coordinate grid to use to get them. The lesson includes some problems from a real-life context.

Q1:

Consider the two points and .

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

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

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 .

A4 length units
B length units
C length units
D length units
E16 length units

Q5:

Find the distance between the points and .

A length units
B length units
C length units
D length units
E21 length units

Q6:

Find the distance between the points and .

A length units
B3 length units
C length units
D length units
E13 length units

Q7:

Find the distance between the points and .

A length units
B length units
C length units
D length units
E14 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?

Q14:

Given , , and , what is the perimeter of ?

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:

William 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:

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 .

Q19:

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

Q20:

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.

Q21:

On a map, each coordinate represents a distance in miles from some fixed point. San Jose’s coordinates are (76, ), while those for San Francisco are (53, 17). Find the distance between San Jose and San Francisco to the nearest mile.

Q22:

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 .

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

Find an expression for the coordinates of .