Question

Line L1 is passing through $(1,2)$ and $(2,1)$.
Line L2 is passing through $(2,4)$ and $(1,3)$.
Which of the following is/are true?

• A. Line 1 and Line 2 are perpendicular to each other
• B. Line 1 and Line 2 are parallel to each other
• C. Line 1 and Line 2 are a linear functions
• D. Line 1 and Line 2 are a non-linear functions

Answer 1

Answer: (A), (C)

Line 1 and Line 2 are a linear functions

Step 1: Find the slope of line L1.
Given, Line L1 is passing through $(1,2)$ and $(2,1)$.

Slope of the line segment =$\frac{y_2-y_1}{x_2-x_1}$
The points of line 1 are
$(x_1,y_1)\equiv (1,2)$
$(x_2,y_2)\equiv (2,1)$
$\therefore$ Slope of line L1 $=\frac{1-2}{2-1}=-1$

Step 2: Similarly, find the slope of line L2.
Given, Line L2 is passing through $(2,4)$ and $(1,3)$.
$(x_1,y_1)\equiv (2,4)$
$(x_2,y_2)\equiv (1,3)$
$\therefore$ Slope of line L2 $=\frac{3-4}{1-2}=\frac{-1}{-1}=1$

Hence, Slope of line L1 $\times$ Slope of line L2 $=-1\times 1=-1$
Hence, L1 is perpendicular to L2 and vice versa.

$\to$To check whether L1 and L2 are linear function or not.
Linear function: The function whose graph is a straight line.
Non-linear function: The function whose graph is not a straight line.

Hence the two lines L1 and L2 are linear function.
Option (a) and (c) are correct.