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

In this worksheet, we will practice finding the perpendicular distance between a point and a straight line or between two parallel lines on the coordinate plane using the formula.

**Q8: **

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

- A18 or
- B or 3
- C9 or
- D or

**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: **

Find the shortest distance between the line and point .

**Q18: **

Determine the shortest distance between the line and the point .

**Q20: **

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 equations of the two straight lines that satisfy these conditions.

- A,
- B,
- C,
- D,

**Q21: **

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

**Q22: **

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

**Q23: **

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

- A
- B
- C
- D
- E

**Q24: **

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

**Q25: **

Find the shortest distance between the following two parallel lines: If necessary, round your answer to 2 decimal places.