Find the distance between the two points in simplest radical form.    (4,0) and (2,-9)

To find the distance between two points, we use the distance formula:

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

Given points: \((4,0)\) and \((2,-9)\), where \((x_1, y_1) = (4, 0)\) and \((x_2, y_2) = (2, -9)\).

Substitute the values into the formula:

\[
d = \sqrt{(2 - 4)^2 + (-9 - 0)^2}
\]

Simplify the expression:

\[
d = \sqrt{(-2)^2 + (-9)^2}
\]
\[
d = \sqrt{4 + 81}
\]
\[
d = \sqrt{85}
\]

So, the distance between the two points in simplest radical form is \( \sqrt{85} \).

Would you like any further details or explanations?

Here are some related questions you might find helpful:
1. How do you calculate the midpoint between two points?
2. What is the equation of a line passing through two points?
3. How do you convert the distance formula into slope-intercept form?
4. How can you find the distance between two points on a 3D plane?
5. How can you verify if two points lie on the same circle?

**Tip:** Remember, the distance formula is derived from the Pythagorean theorem applied to the differences in coordinates!

Find the distance between the two points in simplest radical form. (4,0) and (2,-9)

Learn how to calculate the distance between two points (4,0) and (2,-9) using the distance formula in coordinate geometry. This step-by-step solution demonstrates key concepts such as the distance formula and Pythagorean theorem, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation