# Worksheet: Perpendicular Distance from a Point to a Line on the Coordinate Plane

In this worksheet, we will practice finding the perpendicular distance between a point and a straight line in the coordinate plane using the formula.

Q1:

Determine the length of the perpendicular from a point to the line .

• A
• B
• C
• D
• E0

Q2:

Find the length of the perpendicular drawn from the origin to the straight line rounded to the nearest hundredth.

• A4.20 length units
• B14.85 length units
• C0.24 length units
• D21.00 length units

Q3:

Find the length of the perpendicular from the point to the -axis.

Q4:

Find the length of the perpendicular from the point to the -axis.

Q5:

Find the length of the perpendicular drawn from the point to the straight line .

• A length units
• B length units
• C length units
• D length units

Q6:

Find the length of the perpendicular drawn from the point to the straight line passing through the points and .

• A units length
• B units length
• C units length
• D units length

Q7:

If the length of the perpendicular drawn from the point to the straight line is 10 length units, find all the possible values of .

• A or
• B or
• C or
• D or

Q8:

Find all values of for which the distance between the line and point is .

• A18 or
• B or 3
• C9 or
• D or

Q9:

Find the length of the perpendicular line drawn from the point to the straight line that passes through the point and whose slope is .

• A length units
• B length units
• C length units
• D length units

Q10:

What is the distance between the point and the line of slope 1 through ?

• A length units
• B length units
• C length units
• D length units

Q11:

Find the perpendicular distance between the point and the -axis.

Q12:

If the length of the perpendicular drawn from the point to the straight line equals , find all possible values of .

• A83 or
• B or
• C or
• D83 or
• E57 or 9

Q13:

Suppose and are equal chords in a circle , where the coordinates of points , , and are , , and , respectively. Find the distance between chord and .

• A2
• B
• C
• D4

Q14:

What is the distance between lines and ?

• A
• B
• C
• D

Q15:

What is the distance between the point and the -axis?

• A length units
• B20 length units
• C length units
• D6 length units

Q16:

Find the shortest distance between the line and point .

Q17:

Find the shortest distance between the line and the point .

• A
• B
• C
• D
• E

Q18:

Find the shortest distance between the point and the line which passes through the points and .

• A
• B
• C
• D
• E

Q19:

Determine the shortest distance between the line and the point .

Q20:

Find the length of the perpendicular drawn from the point to the straight line passing through the points and .

• A units length
• B units length
• C units length
• D units length

Q21:

If the length of the perpendicular from the point to a straight line is 2 length units, where the vector is the direction vector of the straight line. Determine the equation of the straight line.

• A,
• B,
• C,
• D,

Q22:

Calculate the area of the circle of center that is tangent to the line . Give your answer to the nearest hundredth.

Q23:

Determine the shortest distance between the two parallel lines whose equations are and .

Q24:

Find the shortest distance between the two parallel lines with equations and .

• A
• B
• C
• D
• E

Q25:

The distance between two parallel lines is . If a third line is perpendicuar to both these lines, and intersects them at the points and , find all possible values of .

• A or
• B or
• C or
• D or
• E or