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

**Q1: **

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

- A0
- B
- C
- D
- E

**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 .

- A or 3
- B or
- C18 or
- D9 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 .

- A or
- B or
- C83 or
- D57 or 9
- E83 or

**Q13: **

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

- A4
- B
- C
- D2

**Q14: **

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

**Q15: **

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.

**Q16: **

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

**Q17: **

What is the distance between lines and ?

- A
- B
- C
- D

**Q18: **

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

- A length units
- B20 length units
- C6 length units
- D length units

**Q19: **

Find the shortest distance between the line and point .

**Q20: **

Find the shortest distance between the line and the point .

- A
- B
- C
- D
- E

**Q21: **

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

**Q22: **

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

- A
- B
- C
- D
- E

**Q23: **

Determine the shortest distance between the line and the point .

**Q24: **

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

**Q25: **

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