Find the distance between the points \( (3,0) \) and \( (5,4) \) Distance \( =\square \)

To find the distance between the points \( (3,0) \) and \( (5,4) \), you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the values: \[ d = \sqrt{(5 - 3)^2 + (4 - 0)^2} = \sqrt{(2)^2 + (4)^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} \] So, the distance is \( 2\sqrt{5} \). A fun way to visualize this is to imagine a tiny ant that wants to travel from point \( (3,0) \) to \( (5,4) \). Instead of wandering around, it takes the shortest path, like a tiny superhero on a mission! The distance it travels, \( 2\sqrt{5} \), is just about 4.47 units. Who knew that a small journey could have such a heroic twist? When calculating distances between two points, it's crucial not to rush your work. A common mistake is forgetting to square the differences before adding them. Maybe you're thinking, "Ah, those numbers look so simple!" But remember, they can turn complicated if not handled correctly! Always double-check your values before taking the square root—it's like a safety net for your calculations!