Derive the formula for the angle between two straight lines with slopes hence find the slope of the line which makes an angle with the line
Answers
Answer:
Step-by-step explanation:
The measure of steepness and direction of a straight line is given by its slope. The slope is usually represented by the letter m. In the given figure, if the angle of inclination of the given line with the x-axis is θ then, the slope of the line is given by tan θ.
Slope of a Line
The slope of a line is given as m = tan θ. If two points A (x1,y1) and B (x2,y2) lie on the line with (x1 ≠ x2) then the slope of the line AB is given as:
m = tan θ = y2 − y1x2 − x1
Where θ is the angle which the line AB makes with the positive direction of the x-axis. θ lies between 0° and 180°
It must be noted that θ = 90° is only possible when the line is parallel to y-axis i.e. at x1 = x2, at this particular angle the slope of the line is undefined.
Conditions for perpendicularity, parallelism, and collinearity of straight lines