NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 .