In this worksheet, we will practice finding the equation of a straight line in parametric form using a point on the line and the vector direction of the line.

**Q3: **

Consider the line shown that passes through the point and makes an angle of 45 degrees with the positive -axis.

Suppose that the distance between and any point on the line is .

Write, in terms of , an expression for the horizontal distance between the two points.

- A
- B
- C
- D

Write, in terms of , an expression for the vertical distance between the two points.

- A
- B
- C
- D

Hence, write a pair of parametric equations which describe the line.

- A ,
- B ,
- C ,
- D ,

Find the coordinates of the point on the line which is at a distance of 4 from .

- A
- B
- C
- D

**Q4: **

Write a pair of parametric equations with parameter describing the shown line.

- A ,
- B ,
- C ,
- D

**Q5: **

Write the parametric equation of the straight line that passes through the point and makes an angle of with the positive -axis as shown.

- A
- B
- C
- D

**Q6: **

The equations parameterize the line segment between and over the interval .

Which of the following is a parameterization of the line segment on ?

- A
- B
- C
- D
- E

Which of the following is a parameterization of the line segment on that starts at and ends at ?

- A
- B
- C
- D
- E

Which of the following is a parameterization of the line segment on ?

- A
- B
- C
- D
- E

If the parameterizations you have given above correspond to a particle moving along the line segment, how does the parameterization over interval relate to the one over ?

- AOver , the particle is moving half as fast as over .
- BOver , the particle is moving three times as fast as over .
- COver , the particle is moving twice as fast as over .
- DOver , the particle is moving one-third as fast as over .

**Q7: **

Consider the points , and and the line segments in the figure.

Give the parameterization of over the interval .

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

Give the parameterization of over the interval .

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

Find functions and defined for so that , parameterizes the given path from to .

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

**Q8: **

Let and . Which of the following is a parameterization of over that starts at and ends at .

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

**Q9: **

Let and . Which of the following is a parameterisation of over that starts at and ends at .

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

**Q10: **

Find the parameterization , of the path using the interval .

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

**Q11: **

Let and . Find the parameterisation of over that starts at and ends at .

- A
- B
- C
- D
- E

**Q12: **

A cube with side 3 sits with a vertex at the origin and three sides along the positive axes. Find the parametric equations of the main diagonal from the origin.

- A , ,
- B , ,
- C , ,
- D , ,

**Q13: **

True or False: There is only one way to parameterize the line segment from to .

- Afalse
- Btrue