Use the Pythagorean theorem to find the distance between points (3, 4) and (7, 1) in the Cartesian plane

• Point 1: $(x_1, y_1) = (3, 4)$
• Point 2: $(x_2, y_2) = (7, 1)$

• $\Delta x = x_2 - x_1 = 7 - 3 = 4$
• $\Delta y = y_2 - y_1 = 1 - 4 = -3$

The distance $d$ between two points is given by the formula $d = \sqrt{(\Delta x)^2 + (\Delta y)^2}$.

• $d = \sqrt{(4)^2 + (-3)^2}$
• $d = \sqrt{16 + 9}$
• $d = \sqrt{25}$
• $d = 5$