Find distance between the given pair of points. (5.2) and \( (-7 .-3) \)

To find the distance between the points (5, 2) and (-7, -3), we use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the values, we have: \[ d = \sqrt{((-7) - 5)^2 + ((-3) - 2)^2} = \sqrt{(-12)^2 + (-5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \] So the distance between the points is 13 units. When using the distance formula, always double-check your signs! A simple mistake in the coordinates can change your calculations significantly. Remember, \( x_2 \) and \( x_1 \) should always correspond to the same points to avoid any mix-ups. Getting comfortable with the distance formula can really enhance your understanding of geometry! If you're interested in exploring further, consider checking out interactive geometry tools online, or textbooks on coordinate geometry that delve deeper into relationships between points, lines, and shapes in more complex dimensions.