## If the Points a 3 5 and b 1 4

Have you ever wondered how to calculate the distance between two points on a graph? It’s a common question in geometry, and there are a few different ways to approach it. In this article, we’ll show you how to find the distance between two points a (3,5) and b (1,4) using the distance formula.

The distance formula is a mathematical equation that can be used to calculate the distance between any two points on a coordinate plane. The formula is:

$$ d = \sqrt(x_2 – x_1)^2 + (y_2 – y_1)^2$$

Where:

- (x1, y1) are the coordinates of the first point
- (x2, y2) are the coordinates of the second point
- d is the distance between the two points

To find the distance between points a (3,5) and b (1,4), we can simply plug the values into the distance formula:

$$ d = \sqrt(1 – 3)^2 + (4 – 5)^2$$

$$ d = \sqrt(-2)^2 + (-1)^2$$

$$ d = \sqrt4 + 1$$

$$ d = \sqrt5$$

$$ d = 2.236$$

Therefore, the distance between points a (3,5) and b (1,4) is 2.236 units.

### Latest Trends and Developments

The distance formula is a fundamental concept in geometry, and it has been used for centuries to solve a variety of problems. In recent years, the distance formula has been used in a number of new and innovative ways, such as:

- In computer graphics, the distance formula is used to calculate the distance between objects in 3D space. This information can be used to create realistic images and animations.
- In robotics, the distance formula is used to calculate the distance between a robot and its target. This information can be used to control the robot’s movement and ensure that it reaches its destination safely.
- In medicine, the distance formula is used to calculate the distance between tumors and other organs. This information can be used to plan radiation therapy and other treatments.

### Tips and Expert Advice

Here are a few tips and expert advice for using the distance formula:

- Make sure that the coordinates of the two points are correct. If the coordinates are incorrect, the distance formula will give you an incorrect answer.
- Be careful when using the square root function. The square root function can give you an imaginary number if the input is negative. If the input is negative, you should take the absolute value of the input before using the square root function.
- The distance formula can be used to find the distance between any two points on a coordinate plane. However, the distance formula cannot be used to find the distance between two points in 3D space.

### FAQ

Here are some frequently asked questions about the distance formula:

**What is the distance formula?****How do I use the distance formula?****What are some applications of the distance formula?**- Calculating the distance between two objects in 3D space
- Controlling the movement of a robot
- Planning radiation therapy and other medical treatments
**What are some tips for using the distance formula?**- Make sure that the coordinates of the two points are correct.
- Be careful when using the square root function.
- The distance formula can be used to find the distance between any two points on a coordinate plane. However, the distance formula cannot be used to find the distance between two points in 3D space.

The distance formula is a mathematical equation that can be used to calculate the distance between any two points on a coordinate plane. The formula is: $$ d = \sqrt(x_2 – x_1)^2 + (y_2 – y_1)^2$$

To use the distance formula, simply plug the coordinates of the two points into the formula and solve for d. For example, to find the distance between the points (3,5) and (1,4), you would plug these values into the distance formula and solve for d:

$$ d = \sqrt(1 – 3)^2 + (4 – 5)^2$$

$$d = \sqrt(-2)^2 + (-1)^2$$

$$d = \sqrt4 + 1$$

$$d = \sqrt5$$

$$d = 2.236$$

The distance formula has a wide range of applications, including:

Here are a few tips for using the distance formula:

### Conclusion

The distance formula is a powerful tool that can be used to solve a variety of problems. By understanding the distance formula and how to use it, you can gain a deeper understanding of geometry and its applications.

Are you interested in learning more about the distance formula? If so, please leave a comment below and I will be happy to answer any questions you have.

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