Question

enter the correct answer that completes the sentence below. the distance from the origin to the point (-24, 32) is \boxed{}.

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). The origin is \((0, 0)\), so \( x_1 = 0 \), \( y_1 = 0 \), \( x_2=-24 \), \( y_2 = 32 \).

Step2: Substitute values into formula

Substitute the values into the formula: \( d=\sqrt{(-24 - 0)^2+(32 - 0)^2}=\sqrt{(-24)^2 + 32^2} \).

Step3: Calculate squares

Calculate \((-24)^2=576\) and \(32^2 = 1024\). Then \( d=\sqrt{576 + 1024} \).

Step4: Add inside the square root

Add \(576+1024 = 1600\). So \( d=\sqrt{1600} \).

Step5: Simplify square root

\(\sqrt{1600}=40\).

Answer:

40