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?

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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.