NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 8

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1. In what ratio, the line joining and is divided by the line ?

Answer:

The equation of the line joining the points is given by

……………………… eq (1)

The equation of the given line is

…………….. eq (2)

The point of intersection of lines equation (1) and (2) is given by

Consider point divide the line segment joining in the ratio . Accordingly, by section formula,

So, the line joining the points and is divided by line in the ratio .

2. Find the distance of the line from the point along the line .

Answer:

The given lines are

………………………… eq (1)

…………………… eq (2)

is a point on line (1).

Consider be the point of intersection of lines equation (1) and (2).

On solving equations (1) and (2),

and

Coordinates of point are

By using distance formula, the distance between points can be obtained as

.

.

So, the required distance is .