Question

If two lines are anti-parallel then their slopes?
A. are equal
B. are opposite
C. product of slopes are $ - 1$
D. Both A and B

Answer 1

Hint:If two lines are anti-parallel, that means they are extending in opposite directions and have a constant distance between them till infinity. Now, if we think about slopes of anti-parallel lines, they have the same slopes as that of the parallel lines. The difference between parallel and antiparallel lines is the direction of lines with respect to one another.

Complete answer:
In the above question, we have to find the slopes of two anti-parallel lines. The slope of a line is defined as the change in value of y for each unit change in value of x. Slope of a line is determined by the angle made by the line with the positive x-axis. It is calculated as the tangent of the angle made by the line with the positive x-axis.

We know that the slope of two parallel lines is equal because they have a constant distance between them. Thus, there is no change in the inclination of both the lines with the x-axis.
We also know that the only difference between parallel lines and antiparallel lines is the direction of one line with respect to the other.

In parallel lines both have the same direction, but in case of antiparallel lines the direction is opposite with respect to one another. But the distance remains the same in case of antiparallel lines.So, the slope of antiparallel lines would also be the same as parallel lines.

Therefore, the slope of antiparallel lines is also equal.

Note:These questions are based on the properties of the particular topic. If we applied the properties correctly the question will never be long before doing such a question.In case of finding slope only the slope of parallel lines and perpendicular lines are interconnected, one having similar slope while the other have reciprocal signs with opposite signs with each other.