# 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.

**Table of Contents**

## 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) = [^{b}1^{c}2 -^{b}2^{c}1 /^{a}1^{b}2 -^{a}2^{b}1 ,^{a}2^{c}1 -^{a}1^{c}2 /^{a}1^{b}2 -^{a}2^{b}1]

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) = [^{b}1^{c}2 -^{b}2^{c}1 /^{a}1^{b}2 -^{a}2^{b}1 ,^{a}2^{c}1 -^{a}1^{c}2 /^{a}1^{b}2 -^{a}2^{b}1]

**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.