Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.
Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

Think about \[y\text{ }=\text{ }mx\text{ }+\text{ }c\] as the line going through the point (- 1, 2)

\[2\text{ }=\text{ }m\text{ }\left( -1 \right)\text{ }+\text{ }c\]

So we get

By additional computation

\[2\text{ }=\text{ }-\text{ }m\text{ }+\text{ }c\]

\[c\text{ }=\text{ }m\text{ }+\text{ }2\]

Subbing the worth of c

\[y\text{ }=\text{ }mx\text{ }+\text{ }m\text{ }+\text{ }2\text{ }\ldots \text{ }\left( 1 \right)\]

So the given line is

\[x\text{ }+\text{ }y\text{ }=\text{ }4\text{ }\ldots \text{ }.\text{ }\left( 2 \right)\]

By tackling both the conditions we get

By cross augmentation

\[1\text{ }+\text{ }m2\text{ }=\text{ }m2\text{ }+\text{ }1\text{ }+\text{ }2m\]

So we get

NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines image - 70

\[2m\text{ }=\text{ }0\]

\[m\text{ }=\text{ }0\]

Henceforth, the incline of the necessary line should be zero for example the line should be corresponding to the x-axis