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 .