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In this lesson, we will learn how to find the distance between a point and a straight line in the coordinate plane.

Q1:

Find the length of the perpendicular drawn from the origin to the straight line β 3 π₯ + 4 π¦ β 2 1 = 0 rounded to the nearest hundredth.

Q2:

Find the length of the perpendicular line drawn from the point to the straight line that passes through the point and whose gradient is .

Q3:

Find the length of the perpendicular drawn from the point π΄ ( β 1 , β 7 ) to the straight line passing through the points π΅ ( 6 , β 4 ) and πΆ ( 9 , β 5 ) .

Q4:

Find the length of the perpendicular drawn from the point π΄ ( β 9 , 5 ) to the straight line passing through the points π΅ ( 4 , 3 ) and πΆ ( β 2 , β 7 ) .

Q5:

Find the length of the perpendicular drawn from the point π΄ ( 8 , β 2 ) to the straight line passing through the points π΅ ( β 7 , β 6 ) and πΆ ( 9 , 6 ) .

Q6:

Find the length of the perpendicular drawn from the point π΄ ( β 8 , 1 0 ) to the straight line passing through the points π΅ ( β 3 , β 2 ) and πΆ ( β 8 , 6 ) .

Q7:

If the length of the perpendicular drawn from the point ( β 5 , π¦ ) to the straight line β 1 5 π₯ + 8 π¦ β 5 = 0 is 10 length units, find all the possible values of π¦ .

Q8:

If the length of the perpendicular drawn from the point ( β 8 , π¦ ) to the straight line 3 π₯ + 4 π¦ + 4 = 0 is 8 length units, find all the possible values of π¦ .

Q9:

If the length of the perpendicular drawn from the point ( 8 , π¦ ) to the straight line β 3 π₯ β 4 π¦ + 5 = 0 is 6 length units, find all the possible values of π¦ .

Q10:

If the length of the perpendicular drawn from the point ( 7 , π¦ ) to the straight line 1 2 π₯ β 5 π¦ + 4 = 0 is 9 length units, find all the possible values of π¦ .

Q11:

Find the length of the perpendicular from the point ( β 2 2 , β 5 ) to the π₯ -axis.

Q12:

Find the length of the perpendicular from the point ( 2 9 , 1 1 ) to the π₯ -axis.

Q13:

Find all values of π for which the distance between the line π π₯ + π¦ β 7 = 0 and point ( β 4 , 3 ) is 2 0 β 8 2 4 1 .

Q14:

Find all values of π for which the distance between the line π π₯ β 4 π¦ + 4 = 0 and point ( 3 , β 1 ) is 5 β 1 7 1 7 .

Q15:

Find all values of π for which the distance between the line π π₯ β 6 π¦ + 4 = 0 and point ( 2 , 0 ) is 6 β 6 1 6 1 .

Q16:

Find all values of π for which the distance between the line π π₯ β π¦ + 4 = 0 and point ( β 4 , β 3 ) is β 2 6 2 .

Q17:

Determine the length of the perpendicular from a point π΄ ( π₯ , π¦ ) 1 1 to the line π¦ = 0 .

Q18:

What is the distance between the point and the line of gradient 1 through ?

Q19:

Find the length of the perpendicular drawn from the point π΄ ( 1 , 9 ) to the straight line β 5 π₯ + 1 2 π¦ + 1 3 = 0 .

Q20:

Find the length of the perpendicular drawn from the point π΄ ( β 3 , 5 ) to the straight line 4 π₯ β 2 π¦ + 7 = 0 .

Q21:

Find the length of the perpendicular drawn from the point π΄ ( β 6 , β 8 ) to the straight line 8 π₯ + π¦ + 1 2 = 0 .

Q22:

Find the length of the perpendicular drawn from the point π΄ ( 3 , 7 ) to the straight line β 4 π₯ + 9 π¦ + 6 = 0 .

Q23:

Find the length of the perpendicular drawn from the point π΄ ( 2 , 6 ) to the straight line π₯ + 2 π¦ + 1 0 = 0 .

Q24:

Find the length of the perpendicular from the point ( β 1 9 , β 1 3 ) to the π¦ -axis.

Q25:

Find the length of the perpendicular from the point ( 1 8 , 1 1 ) to the π¦ -axis.

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