Point of Intersection Calculator

The point of intersection calculator instantly finds the point of interaction of two lines residing in the 2-D plan.

The Point of Intersection:

The point of intersection represents the point where two lines are going to interest each other. The intersection points are also known to be the common points on the two lines. The point of intersection of two lines is the point where the lines are going to cross or intersect each other. The two lines only intersect each other when these lines are lying in the same plan. 

How to Find Point of Intersection?

There are two ways to find a point of intersection:

• Substitution method
• Elimination method 

In the following example, we have used the substitution method, finding the value of “x” from the first equation and inserting its value in the second to find the “x” and “y” intercept of the two lines.

Let’s find the points of intersection of the two lines:

2x+3y = 4—————–(1)

3x + 4y = 5——————(2)

Now find the value of x from Eq (1)

2x = -3y + 4——————(1)

Then

x = (-3y + 4)/2————-(3)

Put the value of x in Eq (2)

3(-3y + 4)/2 + 4y = 5

[(-9y + 12)/2]+ 4y = 5

y = 2

Put the value of x in Eq (2)

3x + 4(2) = 5

3x =  5 – 4(2) 

3x =  5 – 8

x =  -3/3

x =  – 1

Working of Point of Intersection Calculator:

Our points of intersection calculator instantly finds the point of intersection for two lines.

 You need to follow the instructions below:

Input:

• Enter the coefficient of x and y 
• Enter the constant values 
• Hit the calculate button 

Output:

• The point of interaction (x,y) of the line
• Graphical representation of points

FAQs:

What Is the Condition for the Intersection of Two Lines?

The necessary condition for the point of intersection of two lines is that this line lies on the same plane. Finding points of intersection, if the line does not lie on the same plan. These lines are not going to intersect each other.

What Is the Common Point of Intersection?

The intersecting lines share a common point and it is also called the point of interaction of two lines. You can find the points of intersection or common points of lines with the points intersection of two lines calculator.

How Do You Write the Intersection of a Line?

There is a special symbol used to denote a point of intersection between two lines. The symbol used to represent the point of intersection is  “∩”. If A and B represent a system or a set of two lines. Then A∩B represents the point of intersection of the lines.

Can the Line of Intersection Make a Right Angle?

Yes, the line of intersection can make a right angle to each other. It means the lines are perpendicular to each other.

References:

From the source of Wikipedia: line intersection,Formulas

From the source of splashlearn.com: Intersecting Lines, Properties