For the points P and​ Q, find the distance​ d(P,Q).
​P(55​,negative 2−2​), ​Q(negative 6−6​,44​)

To find the distance between two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \), we use the distance formula:

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

Given points \( P(55, -2) \) and \( Q(-6, 44) \), the coordinates are:

- \( x_1 = 55 \), \( y_1 = -2 \)
- \( x_2 = -6 \), \( y_2 = 44 \)

Now apply these to the formula:

\[
d(P, Q) = \sqrt{((-6 - 55)^2) + ((44 - (-2))^2)}
\]
\[
= \sqrt{(-61)^2 + (44 + 2)^2}
\]
\[
= \sqrt{3721 + 46^2}
\]
\[
= \sqrt{3721 + 2116}
\]
\[
= \sqrt{5837}
\]

The approximate distance is:

\[
d(P, Q) \approx 76.39
\]

The distance between points \( P \) and \( Q \) is approximately 76.39 units.

Would you like further details or have any questions?

---

Here are 5 related questions:
1. How do you find the midpoint between two points?
2. How would the distance formula change in three-dimensional space?
3. Can you find the slope between points \( P \) and \( Q \)?
4. What are real-world applications of the distance formula?
5. How does the distance formula relate to the Pythagorean theorem?

**Tip:** Always double-check signs when substituting coordinates into the distance formula to avoid common errors.

For the points P and​ Q, find the distance​ d(P,Q). ​P(55​, -2​), ​Q(-6, 44​).

Find the distance between two points P(55, -2) and Q(-6, 44) using the distance formula. This problem covers coordinate geometry concepts and applies the Pythagorean theorem to determine the distance. 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