# Worksheet: Distances between Points and Straight Lines or Planes

In this worksheet, we will practice calculating the perpendicular distance between a point and a straight line or between a point and a plane using a formula for each distance.

Q1:

Find, to one decimal place, the perpendicular distance from point to the line on points and .

Q2:

Find the distance from the point to the plane . Give the result correct to three decimal places.

Q3:

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

• A
• B
• C
• D
• E

Q4:

Find the distance between the point and the plane .

• Alength unit
• Blength units
• Clength units
• Dlength units

Q5:

Find the distance between the two planes and .

• Alength unit
• Blength units
• Clength unit
• Dlength unit

Q6:

Find the distance from the point to the plane : , giving your answer to two decimal places.

Q7:

Find, correct to two decimal places, the distance from the point to the line .

Q8:

Find, correct to two decimal places, the distance from the point to the line .

Q9:

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

• A
• B
• C
• D

Q10:

Find the length of the perpendicular from the origin to the straight line .

• A
• B
• C
• D

Q11:

How far from the -plane is the point ?

Q12:

Find the distance between the point and the plane .

• A length units
• B length units
• C length units
• D17 length units

Q13:

Find, to one decimal place, the perpendicular distance from point to the line on points and .

Q14:

Find, to one decimal place, the perpendicular distance from point to the line on points and .

Q15:

Find the distance between the point and the plane .

• Alength units
• Blength units
• Clength units
• Dlength units

Q16:

Find the distance between the point and the plane .

• Alength units
• Blength units
• Clength units
• Dlength units

Q17:

Let be the line through point in the direction of vector . Find the distance between and the point , to the nearest hundredth.

Q18:

Let be the line through the point that makes equal angles with the three coordinate axes. What is the distance between the point and , to the nearest hundredth.

Q19:

Determine, to the nearest hundredth, the length of the perpendicular drawn from the point to the straight line .

Q20:

Determine, to the nearest hundredth, the distance between the point , the straight line passing through the point , and its direction ratios .

Q21:

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

Q22:

Find, to the nearest hundredth, the distance between the parallel lines and .