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

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

The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the distance formula, \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\), which is Pythagoras’ theorem applied to the horizontal and vertical gaps between the points.

• A\((-5,7)\) and B\((-1,3)\)

• Horizontal gap: \(x_2-x_1=-1-(-5)=4\)

• Vertical gap: \(y_2-y_1=3-7=-4\)

• \(d=\sqrt{4^2+(-4)^2}=\sqrt{16+16}=\sqrt{32}\)

• \(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\) units

The gaps are squared, so the minus sign of \(-4\) does not matter; a distance is never negative.