Secant lines


In the field of geometry when we refer to a line we are referring to the one-dimensional line that, formed by an infinite number of points, extends in the same direction . A secant line or straight , which can also be simply called a secant, is a line that passes through two points on a curve . When the two points meet or, more precisely, when one approaches the other, the secant line tends to a tangent line .


What is a secant line?

secant line is a line that cuts a curve at two different points which as they get closer , and their distance is reduced to zero , the line then acquires the name of a secant line.

  • Definition
  • Characteristics of secant lines
  • Types of secant lines
  • Objects with intersecting lines
  • Examples


In the area of mathematics we know intersecting lines as those lines that are found by cutting a circle at two specific points . As these cutting points get closer, the line also gets closer to the point and because there is only one point that is touching the circumference , it is then called a tangent . In a general way, we can say that a secant line is a line that is located in the same plane that has to be cut at a certain point .


It is important to mention that a line is the union of a series of points which are ordered in the same direction , and this line is given its name by means of a lowercase letter; Depending on the direction of the line, they can also be vertical , horizontal or inclined ; and depending on their relative position we can find the parallel lines that do not intersect and the secants that do, forming 90º angles .

The secant line is the line that is found connecting two points (x, f (x)) and (a, f (a)) on the Cartesian plane on a curve described by a function y = f (x). Give the average rate of change of f from x to.

Characteristics of secant lines

The main characteristics of secant lines are the following:

  • If the two points are very close together , the secant line is almost the same as a tangent line .
  • When the lines intersect , they give rise to four different regions called angles .
  • Secant lines are not equidistant .
  • They are straight lines that intersect each other.

Types of secant lines

Regarding the types or the classification of secant lines, we can say that they can be classified as oblique and perpendicular . Oblique secant lines can be defined as those lines that intersect at a certain point forming angles equal to two by two, that is, they form two equal or similar obtuse angles and two equal or similar acute angles because they are opposite or opposite.

Secondly, we find the perpendicular lines , these types of lines also intersect at a single point with the peculiarity that the angles that are formed in it are straight, that is, they are 90º angles and, furthermore, the four are totally equal or similar . On the contrary, when two lines do not have any points in common , and they are in the same plane, they are called parallel lines .

In abstract mathematics , the points connected by a secant line can be real or complex imaginary conjugates .

Objects with intersecting lines

We can observe intersecting lines in the world around us. Basically anywhere you see a curve with a line that intersects two or more points, we have a secant line.

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