The distance between points A(-5, 7) and B(-1, 3) is:

The correct answer is Option (3) → $4\sqrt{2}$ units

To find the distance between two points $A(x_1, y_1)$ and $B(x_2, y_2)$, we use the Distance Formula, which is derived from the Pythagorean theorem:

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

1. Identify the Coordinates

• Point $A(x_1, y_1) = (-5, 7)$
• Point $B(x_2, y_2) = (-1, 3)$

2. Substitute into the Formula

$d = \sqrt{(-1 - (-5))^2 + (3 - 7)^2}$

Simplify the terms inside the parentheses:

• $-1 - (-5) = -1 + 5 = 4$
• $3 - 7 = -4$

3. Calculate the Squares and Root

$d = \sqrt{(4)^2 + (-4)^2}$

$d = \sqrt{16 + 16}$

$d = \sqrt{32}$

4. Simplify the Radical

We can simplify $\sqrt{32}$ by finding the largest square factor:

$d = \sqrt{16 \times 2}$

$d = 4\sqrt{2}$