24. Find the distance between \( A(0,3) \) and \( B(4,5) \). \( (2 \text { Points })^{*} \) 4.47 8.94 20 35

To find the distance between points \( A(0,3) \) and \( B(4,5) \), we use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting in our points \( A \) and \( B \): \[ d = \sqrt{(4 - 0)^2 + (5 - 3)^2} = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20} \approx 4.47 \] So the distance is approximately \( 4.47 \). The forms of this distance formula have been around since the ancient Greeks! Euclid, in his writings, laid down the basics of geometry, including how to measure distance in a two-dimensional plane. Fast forward to today, and it becomes essential for everything from navigation to GPS technology, making it possible to pinpoint locations with incredible accuracy. Isn't it amazing how math from ancient times still plays a crucial role in our modern world? If you ever find yourself confused by distance calculations, remember this helpful tip: double-check the coordinates you’re plugging in. A common mistake is to mix up the x and y values or even forget to square the differences! Visualization can also be a lifesaver—drawing a quick sketch can help you see the actual distance between points, making calculations feel more intuitive and less daunting.