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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:

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

Q2:

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.

Q3:

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

Q4:

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

Q5:

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 .

Q6:

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 ) .

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:

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 .

Q9:

Find the length of the perpendicular line drawn from the point π΄ ( β 8 , 5 ) to the straight line that passes through the point π΅ ( 2 , β 4 ) and whose slope is = β 8 .

Q10:

What is the distance between the point ( β 9 , β 1 0 ) and the line of slope 1 through ( 3 , β 7 ) ?

Q11:

Find the perpendicular distance between the point π΄ ( 2 , 2 0 ) and the π₯ -axis.

Q12:

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

Q13:

Suppose π΄ π΅ and π΄ πΆ are equal chords in a circle π , where the coordinates of points π , π΄ , and π΅ are ( β 9 , 0 ) , ( β 1 1 , β 2 ) , and ( β 7 , β 2 ) , respectively. Find the distance between chord π΄ πΆ and π .

Q14:

Let πΏ be the line through point ( 7 , 5 , 5 ) in the direction of vector ( 2 , 4 , β 9 ) . Find the distance between πΏ and the point ( 2 , 6 , 6 ) , to the nearest hundredth.

Q15:

Let πΏ be the line through the point ( β 6 , 8 , 9 ) that makes equal angles with the three coordinate axes. What is the distance between the point ( β 4 , 5 , 3 ) and πΏ , to the nearest hundredth.

Q16:

Determine, to the nearest hundredth, the length of the perpendicular drawn from the point ( β 5 , β 7 , β 1 0 ) to the straight line π₯ + 8 2 = π¦ β 9 8 = π§ + 7 β 8 .

Q17:

What is the distance between lines ( β 1 6 , β 1 6 ) + π ( 2 , 4 ) and ( 1 9 , β 1 7 ) + π ( 7 , 1 4 ) ?

Q18:

What is the distance between the point ( 1 6 , 1 2 , 2 0 ) and the π¦ -axis?

Q19:

Find the shortest distance between the line π¦ = 1 and point π΄ ( 1 , 7 ) .

Q20:

Find the shortest distance between the line π¦ = 1 2 π₯ β 2 and the point π΄ ( 9 , β 1 0 ) .

Q21:

Determine, to the nearest hundredth, the distance between the point ( 7 , β 5 , β 4 ) , the straight line passing through the point ( 0 , β 2 , 2 ) , and its direction ratios ( β 9 , 7 , β 5 ) .

Q22:

Find the shortest distance between the point ( β 6 , 1 0 ) and the line which passes through the points ( 1 , 9 ) and ( 4 , 6 ) .

Q23:

Determine the shortest distance between the line π₯ = 3 and the point π΄ ( β 8 , β 6 ) .

Q24:

Find the length of the perpendicular drawn from point π΄ ( β 8 , 1 , 1 0 ) to the straight line β π = ( β 1 , 2 , β 7 ) + π‘ ( β 9 , β 9 , 6 ) rounded to the nearest hundredth.

Q25:

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 ) .

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