Coordinate Geometry of Straight Line II

Welcome to class! 

In today’s class, we will be talking about coordinate geometry of a straight line. Enjoy the class!

Coordinate Geometry of a Straight Line II

Gradient and Intercepts of a Line | classnotes.ng

Gradient and intercepts of a line

All straight lines have a general equation of the form, where m is the gradient and c is the intercept on the vertical axis.

The gradient (m) of a line is a measure of its slope or steepness. It is defined as a ratio of its vertical displacement, to its horizontal displacement.

m = (y2y1)/(x2x1)
  • Gradient of parallel lines:

Parallel lines have the same slope and so must have the same gradient. That is, lines that have the same gradients are parallel. We can use this fact to prove that any two straight lines are parallel or not.

m1 = m2

coordinate geometry

  • Gradient of perpendicular lines:

The product of the gradients of perpendicular lines is equal to −1. If the product of the gradients of any two lines is −1, then the lines are perpendicular to each other. We can use this fact to prove that and two straight lines are perpendicular or not.

coordinate geometry

The angle between two intersecting straight lines

The angle between two intersecting straight lines means the measure of the acute angle between the lines.

The angle θ between the lines having slope m1 and m2 is given by

tan θ =  (m2m1)/(1+(m1 × m2))

 

In our next class, we will be talking about Differentiation of algebraic functions. We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

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