# Point of Intersection Calculator

In geometry, you must have seen problems related to lines in terms of particular figures. Being a mathematics student, you must have solved questions related to lines only. It may be simple to solve such problems when you are dealing with lines individually. But it will be hard when you are dealing with two lines joining at a specific point.

Such lines are called intersected lines and the common problem regarding these lines is the calculation of the coordinates of the point of intersection. If you don’t know how to find this particular point, you should use this point of intersection calculator. You can use it to find this point within seconds without making a mistake. you can get these values from this maths calculator just by inserting the entries of the dataset.

## What is the point of intersection?

In mathematics, the point of intersection is the particular point where two lines cut each other. Simply, if two lines join at a particular point, that will be called the point of intersection of those lines. That point will be common for both two lines because they will meet with each other.

The lines that will be intersected must have different angles if drawn on xy plane. If two lines have the same angle (parallel to each other), they will never intersect each other. Similarly, if the intersected lines make an angle of 90 degrees, those lines are called perpendicular to each other.

### What is the point of intersection formula?

To understand the point of intersection formula, you must have to learn about the general form of lines. Normally, a line is represented in the general form as given below:

ax + by + c = 0


In this general formula, a, b, and c represent the constant numbers. If we have two lines in this general form, here is the formula to calculate the point of intersection between those two lines.

Point of intersection (x,y) = [b1c2 - b2c1 /a1b2 - a2b1 , a2c1 - a1c2 /a1b2 - a2b1]


Here, all alphabets with subscript “1” represent the first line while the alphabets with subscript “2” represent the second line.

### How to find the point of intersection?

Calculation of the point of intersection will not be an easy task because of the involvement of multiple values. To let you understand the process properly, we have solved an example here.

Example 1:

Find the point of intersection of lines with the following coordinates, (2, 4, 7) and (5, 7, 11).

Solution:

We can define the given values according to the general formula. After defining and putting values, we get:

Point of intersection (x,y) = [4(11) - 7(7) /2(7) - 5(4) , 5(7) - 2(11) /2(7) - 5(4)]


By solving the equation, we get the following point of intersection.

(x, y) = [5/6 , -13/6]

### How to use the point of intersection calculator?

As the method to find this point is complicated, you can use this online tool of Calculator’s Bag. Here are simple steps you have to follow in this regard.

The steps to use the point of intersection calculator are as follows:

Step 1: Enter the value of the slope of line one in the first required input.

Step 2: Enter the value of the slope of line two in the second required input.

Step 3: Enter the value of an in the third required input.

Step 4: Enter the value of b in the fourth required input.

Step 5: The calculator will automatically display an answer on the screen.

### FAQ | Minimum Maximum Calculator

What is a point of intersection in math?

It is the point where two lines cut each other and make a specific angle.

How to find the point of intersection between two lines?

To find the point of intersection of two lines, you can use the following formula.

Point of intersection (x,y) = [b1c2 - b2c1 /a1b2 - a2b1 , a2c1 - a1c2 /a1b2 - a2b1]


Is the point of intersection the same as the midpoint?

In terms of general lines, the point of intersection will not be the same as the midpoint. But if we discuss it in terms of a parallelogram, the point of intersection of its diagonals will be the midpoint of the whole shape.

Is a point of intersection between a line and a circle?

No, the point of intersection is between two lines. The intersection of a line on a circle has different names according to the nature of the intersection.

What is a point of intersection of two sides of an angle?

The point of intersection of an angle is called the vertex.