Final answer:
The distance between the points (1, -3) and (4, -7) is 5 units, calculated using the distance formula derived from the Pythagorean theorem.
Step-by-step explanation:
To calculate the distance between the points (1, -3) and (4, -7), you can use the distance formula derived from the Pythagorean theorem which is d = \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \). For these points, calculate the differences in the x and y coordinates first: \( \Delta x = 4 - 1 = 3 \) and \( \Delta y = -7 - (-3) = -4 \). Next, square these differences and add them together: \( 3^2 + (-4)^2 = 9 + 16 = 25 \). Finally, take the square root of the sum to get the distance: \( \sqrt{25} = 5 \). Therefore, the distance between (1, -3) and (4, -7) is 5 units.