# Worksheet: Equation of a Straight Line: Parametric Form

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

**Q9: **

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

- A
- B
- C
- D
- E

**Q12: **

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

- AFalse
- BTrue

**Q15: **

In the following figure, if the equation of the straight line is , then the parametric equation of the straight line is .

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

**Q16: **

Straight line passes through the point and has a direction vector . Then, the parametric equations of line are .

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

**Q17: **

The direction vector of the straight line whose parametric equations are and is .

- A
- B
- C
- D

**Q18: **

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

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