**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