distance between (−4,5) and (−9,−7)

To find the distance between the points \((-4, 5)\) and \((-9, -7)\), we use the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the given points into the formula:

\[
\text{Distance} = \sqrt{((-9) - (-4))^2 + ((-7) - 5)^2}
\]

Simplify the expression inside the square root:

\[
\text{Distance} = \sqrt{(-9 + 4)^2 + (-7 - 5)^2} = \sqrt{(-5)^2 + (-12)^2}
\]

Calculate the squares:

\[
\text{Distance} = \sqrt{25 + 144} = \sqrt{169}
\]

Finally, take the square root:

\[
\text{Distance} = 13
\]

So, the distance between the points \((-4, 5)\) and \((-9, -7)\) is 13 units.

Would you like more details or have any questions?

Here are 5 related questions:
1. How can the distance formula be used in three-dimensional space?
2. What is the midpoint between the points \((-4, 5)\) and \((-9, -7)\)?
3. What is the equation of the line passing through the points \((-4, 5)\) and \((-9, -7)\)?
4. How do you calculate the distance between two points using vectors?
5. What would be the distance if the points were \((-4, -5)\) and \((-9, 7)\)?

**Tip:** When working with negative coordinates, be careful with signs when performing subtraction in the distance formula.

Learn how to calculate the distance between the points (-4, 5) and (-9, -7) using the distance formula. Understand the steps involved and solve similar problems with ease. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation