Answer
Option (A) is correct .
Reason
The formula for the slope.
\(Slope = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
As given
Line AB contains (0, 4) and (1, 6) .
put in the slope formula
\(Slope = \frac{6 - 4}{1 - 0}\)
\(Slope = \frac{2}{1}\)
Slope of the AB is 2.
As given
Line CD contains points (2, 10) and (−1, 4).
put in the slope formula
\(Slope = \frac{4 - 10}{-1 -2}\)
\(Slope = \frac{-6}{-3}\)
Slope = 2
Slope of the CD is 2.
As the slope of the AB contains (0, 4) and (1, 6) Line CD contains points (2, 10) and (−1, 4) is 2 .
Therefore the option (A) is correct i.e the lines are parallel because the slopes are the same.
