NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 3

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Distance between point and line

Distance Between Point and Line

Distance between point and line

1. What are the points on the y-axis whose distance from the line is units.

Answer:

Consider be the point on the y-axis whose distance from line is 4 units.

The given line can be written as

………………….… eq (1)

On comparing equation (1) to the general equation of line ,

.

It is known that the perpendicular distance (d) of a line from a point = is given by

So, if (0, b) is the point on the y-axis whose distance from line is 4 units, then:

So, the required points are

2. Find the perpendicular distance from the origin to the line joining the points

Answer:

The equation of the line joining the points is given by

It is known that the perpendicular distance (d) of a line from a point is given by

So, the perpendicular distance (d) of the given line from point is