Find the distance between the two points in simplest radical form.
left parenthesis, minus, 2, comma, minus, 7, right parenthesis, and , left parenthesis, 5, comma, 0, right parenthesis
(−2,−7) and (5,0)

To find the distance between the two points \((-2, -7)\) and \((5, 0)\), you can use the distance formula:

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

where \((x_1, y_1)\) is \((-2, -7)\) and \((x_2, y_2)\) is \((5, 0)\).

Substituting the values into the formula:

\[
d = \sqrt{(5 - (-2))^2 + (0 - (-7))^2}
\]

Simplify the expressions inside the square root:

\[
d = \sqrt{(5 + 2)^2 + (0 + 7)^2}
\]

\[
d = \sqrt{7^2 + 7^2}
\]

\[
d = \sqrt{49 + 49}
\]

\[
d = \sqrt{98}
\]

Simplify \(\sqrt{98}\):

\[
d = \sqrt{49 \times 2}
\]

\[
d = 7\sqrt{2}
\]

So, the distance between the two points in simplest radical form is:

\[
\boxed{7\sqrt{2}}
\]

Would you like any more details or have any questions? Here are some related questions that might interest you:

1. How do you simplify radicals like \(\sqrt{98}\)?
2. What is the distance formula, and why does it work?
3. How can you find the midpoint between two points?
4. What are some applications of the distance formula in geometry?
5. How do you find the length of a line segment on a coordinate plane?

**Tip:** Always simplify your radicals as much as possible to express the answer in the simplest form!

Learn how to calculate the distance between two points (-2, -7) and (5, 0) using the distance formula and simplifying the result to radical form. This problem covers key concepts in coordinate geometry, including the distance formula and simplification of radicals. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation