# Worksheet: Distance on the Coordinate Plane: Pythagorean Formula

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.

- A8
- B2
- C
- D6
- E

**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 ?

- A
- B
- C
- D18

**Q8: **

Find the distance between the points and .

- A length units
- B length units
- C13 length units
- D length units
- E3 length units

**Q9: **

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

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

**Q10: **

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

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

**Q11: **

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

**Q12: **

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.

**Q13: **

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

**Q14: **

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 rescue boat
- BThe coast guard craft

**Q17: **

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
- BNo
- CIt is impossible to tell.

**Q18: **

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

- A
- B

**Q19: **

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

- A
- B
- C
- D7
- E

**Q20: **

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

- A53
- B9
- C
- D
- E

**Q21: **

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

**Q22: **

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

**Q23: **

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

**Q24: **

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

**Q25: **

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