# 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 .

**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

**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 .