Find the distance d left parenthesis Upper P 1 comma Upper P 2 right parenthesis between the points Upper P 1 and Upper P 2 .
Upper P 1 equals left parenthesis negative 5 comma 3 right parenthesis​; Upper P 2 equals left parenthesis 2 comma 6 right parenthesis

To find the distance \( d(P_1, P_2) \) between the points \( P_1(-5, 3) \) and \( P_2(2, 6) \), we use the distance formula:

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

Here:
- \( P_1(x_1, y_1) = (-5, 3) \)
- \( P_2(x_2, y_2) = (2, 6) \)

Now, substitute the coordinates into the formula:

\[
d = \sqrt{(2 - (-5))^2 + (6 - 3)^2}
\]

Simplify the terms:

\[
d = \sqrt{(2 + 5)^2 + (6 - 3)^2} = \sqrt{7^2 + 3^2}
\]

\[
d = \sqrt{49 + 9} = \sqrt{58}
\]

Thus, the distance between \( P_1 \) and \( P_2 \) is:

\[
d = \sqrt{58} \approx 7.62
\]

Would you like more details, or do you have any questions?

Here are five related questions:
1. What is the distance between \( P_1(0, 0) \) and \( P_2(3, 4) \)?
2. Can you derive the distance formula from the Pythagorean theorem?
3. How does the distance formula apply in three-dimensional space?
4. What is the midpoint between \( P_1(-5, 3) \) and \( P_2(2, 6) \)?
5. How do you calculate the slope between two points in a coordinate plane?

**Tip:** Always double-check your signs when plugging coordinates into the distance formula to avoid mistakes.

Find the distance d(P1, P2) between the points P1 and P2. P1 = (-5, 3); P2 = (2, 6).

Learn how to find the distance between two points P1(-5, 3) and P2(2, 6) using the distance formula √((x2 - x1)^2 + (y2 - y1)^2). This problem involves geometry and the Pythagorean theorem. Suitable for students in Grades 9-12.

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