Find The Distance Between The Points { (-6, -7)$}$ And { (-4, -2)$}$.The Distance Between The Two Points Is { \square$}$ Unit(s).(Simplify Your Answer. Type An Exact Answer, Using Radicals As Needed.)

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Introduction

In mathematics, the distance between two points in a coordinate plane is an essential concept that is used in various fields such as geometry, trigonometry, and physics. The distance between two points can be calculated using the distance formula, which is derived from the Pythagorean theorem. In this article, we will discuss how to find the distance between two points in a coordinate plane using the distance formula.

The Distance Formula

The distance formula is a mathematical formula that is used to calculate the distance between two points in a coordinate plane. The formula is as follows:

d=(x2βˆ’x1)2+(y2βˆ’y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

where dd is the distance between the two points, (x1,y1)(x_1, y_1) is the coordinates of the first point, and (x2,y2)(x_2, y_2) is the coordinates of the second point.

Step-by-Step Solution

To find the distance between the points {(-6, -7)$}$ and {(-4, -2)$}$, we can use the distance formula. Here are the step-by-step solutions:

Step 1: Identify the Coordinates of the Two Points

The coordinates of the two points are given as {(-6, -7)$}$ and {(-4, -2)$}$.

Step 2: Plug in the Values into the Distance Formula

We can plug in the values of the coordinates into the distance formula as follows:

d=((βˆ’4)βˆ’(βˆ’6))2+((βˆ’2)βˆ’(βˆ’7))2d = \sqrt{((-4) - (-6))^2 + ((-2) - (-7))^2}

Step 3: Simplify the Expression

We can simplify the expression by evaluating the expressions inside the parentheses:

d=(2)2+(5)2d = \sqrt{(2)^2 + (5)^2}

Step 4: Calculate the Squares

We can calculate the squares of the expressions:

d=4+25d = \sqrt{4 + 25}

Step 5: Add the Numbers

We can add the numbers inside the square root:

d=29d = \sqrt{29}

Step 6: Simplify the Square Root

We can simplify the square root by finding the square root of the number:

d=29d = \boxed{\sqrt{29}}

Conclusion

In this article, we discussed how to find the distance between two points in a coordinate plane using the distance formula. We used the distance formula to find the distance between the points {(-6, -7)$}$ and {(-4, -2)$}$. The distance between the two points is {\sqrt{29}$}$ unit(s).

Final Answer

Introduction

In our previous article, we discussed how to find the distance between two points in a coordinate plane using the distance formula. In this article, we will answer some frequently asked questions (FAQs) about finding the distance between two points.

Q&A

Q: What is the distance formula?

A: The distance formula is a mathematical formula that is used to calculate the distance between two points in a coordinate plane. The formula is as follows:

d=(x2βˆ’x1)2+(y2βˆ’y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Q: How do I use the distance formula?

A: To use the distance formula, you need to identify the coordinates of the two points, plug in the values into the formula, simplify the expression, and calculate the square root.

Q: What if the coordinates are negative?

A: If the coordinates are negative, you can simply plug in the values into the formula and simplify the expression. For example, if the coordinates are (-6, -7) and (-4, -2), you can plug in the values into the formula as follows:

d=((βˆ’4)βˆ’(βˆ’6))2+((βˆ’2)βˆ’(βˆ’7))2d = \sqrt{((-4) - (-6))^2 + ((-2) - (-7))^2}

Q: Can I use the distance formula to find the distance between two points in 3D space?

A: Yes, you can use the distance formula to find the distance between two points in 3D space. However, you need to use the 3D distance formula, which is as follows:

d=(x2βˆ’x1)2+(y2βˆ’y1)2+(z2βˆ’z1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}

Q: How do I simplify the expression in the distance formula?

A: To simplify the expression in the distance formula, you need to evaluate the expressions inside the parentheses, calculate the squares, and add the numbers.

Q: Can I use a calculator to find the distance between two points?

A: Yes, you can use a calculator to find the distance between two points. Simply plug in the values into the formula and calculate the square root.

Q: What if the distance is not a whole number?

A: If the distance is not a whole number, you can simplify the square root by finding the square root of the number. For example, if the distance is √29, you can simplify it by finding the square root of 29.

Common Mistakes to Avoid

When finding the distance between two points, there are some common mistakes to avoid. Here are some of them:

  • Not identifying the coordinates of the two points: Make sure to identify the coordinates of the two points before plugging in the values into the formula.
  • Not simplifying the expression: Make sure to simplify the expression by evaluating the expressions inside the parentheses, calculating the squares, and adding the numbers.
  • Not using the correct formula: Make sure to use the correct formula for the distance between two points in a coordinate plane.
  • Not checking the units: Make sure to check the units of the distance to ensure that it is in the correct unit.

Conclusion

In this article, we answered some frequently asked questions (FAQs) about finding the distance between two points. We also discussed some common mistakes to avoid when finding the distance between two points. By following the steps and avoiding the common mistakes, you can find the distance between two points with ease.

Final Answer

The final answer is: 29\boxed{\sqrt{29}}