# 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.

Q1:

Find the parametric equations of the straight line that passes through the point with direction vector .

• A,
• B,
• C,
• D,

Q2:

Find the parametric equations of the straight line that makes an angle of with the positive -axis and passes through the point .

• A,
• B,
• C,
• D,

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,

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 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

Q13:

Find the parametric equations of the straight line that passes through the point with direction vector .

• A,
• B,
• C,
• D,

Q14:

The lines , , and , , are parallel. What is ?

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,