Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.
Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.

NCERT Exemplar Solutions for Class 11 Maths Chapter 10 - Image 9

Putting the value of y1 = 4 – x1 in equation 3, we get

\[\begin{array}{*{35}{l}}

4{{x}_{1}}~+\text{ }3\left( 4\text{ }-\text{ }{{x}_{1}} \right)\text{ }=\text{ }5  \\

\Rightarrow ~4{{x}_{1}}~+\text{ }12\text{ }-\text{ }3{{x}_{1}}~=\text{ }5  \\

\Rightarrow ~{{x}_{1}}~=\text{ }5\text{ }-\text{ }12  \\

\Rightarrow ~{{x}_{1}}~=\text{ }-\text{ }7  \\

\end{array}\]

Putting the value of x1 in equation 4, we get

\[\begin{array}{*{35}{l}}

{{y}_{1}}~=\text{ }4\text{ }-\text{ }\left( -7 \right)  \\

\Rightarrow ~{{y}_{1}}~=\text{ }4\text{ }+\text{ }7  \\

\Rightarrow ~{{y}_{1}}~=\text{ }11  \\

\end{array}\]

Hence, the required points on the given line are (3, 1) and (-7, 11)