Find the distance between the points \( (1,2) \) and \( (5,4) \). Radical Form (simplest form): Decimal Form (nearest tenth):

To find the distance between the points \( (1,2) \) 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 \( (x_1, y_1) = (1, 2) \) and \( (x_2, y_2) = (5, 4) \): \[ d = \sqrt{(5 - 1)^2 + (4 - 2)^2} = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5} \] So, the distance in radical form is \( 2\sqrt{5} \). To find the decimal form, calculate \( 2\sqrt{5} \): \[ \sqrt{5} \approx 2.236 \Rightarrow 2\sqrt{5} \approx 2 \times 2.236 \approx 4.472 \] Rounded to the nearest tenth, the distance is approximately \( 4.5 \). **Radical Form (simplest form):** \( 2\sqrt{5} \) **Decimal Form (nearest tenth):** \( 4.5 \)