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.