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

**Q3: **

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.

- A
- B8
- C2
- D
- E6

**Q4: **

What is the distance between the point and the origin?

- A length units
- B length units
- C length units
- D length units

**Q6: **

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

- A
- B
- C
- D

**Q7: **

Given , , and , what is the perimeter of ?

- A18
- B
- C
- D

**Q8: **

How far is the butcher from the garage?

**Q9: **

Find the distance between the points and .

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

**Q10: **

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

- A or
- B or 4
- C or
- D or 4

**Q11: **

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

- A or
- B or
- C or
- D or

**Q12: **

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

**Q13: **

Nabil 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.

**Q14: **

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

**Q15: **

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

**Q16: **

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.

**Q17: **

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.

**Q18: **

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

**Q19: **

A triangle has vertices at the points , and .

Work out the lengths of the sides of the triangle. Give your answers as surds in their simplest form.

- A , and
- B , and
- C , and
- D , and
- E , and

Is the triangle a right scalene triangle?

- AYes
- BIt is impossible to tell.
- CNo

**Q20: **

The points and have coordinates , and . Which of the line segments and has the greatest length?

- A
- B

**Q21: **

Find the distance between the two points in the figure below, giving your answer in radical form if necessary.

- A
- B7
- C
- D
- E

**Q22: **

Find the distance between the two points in the figure below, giving your answer in radical form if necessary.

- A
- B9
- C53
- D
- E

**Q23: **

Let us consider in a coordinate system of origin . Using the Pythagorean theorem, find the distance between and .

**Q24: **

Let us consider and in a coordinate system of origin . Using the Pythagorean theorem, find the distance between and .

**Q25: **

Let us consider in a coordinate system of origin . Using the Pythagorean theorem, find the distance between and .