Question

enter a number that correctly completes the following statement. the point (12, 5) is units from the origin.

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). The origin is \((0,0)\), and the given point is \((12,5)\).

Step2: Substitute the values into the formula

Substitute \(x_1 = 0,y_1 = 0,x_2=12,y_2 = 5\) into the formula: \(d=\sqrt{(12 - 0)^2+(5 - 0)^2}=\sqrt{12^2 + 5^2}\).

Step3: Calculate the squares

\(12^2=144\) and \(5^2 = 25\). So \(d=\sqrt{144 + 25}\).

Step4: Add the numbers inside the square - root

\(144+25 = 169\). Then \(d=\sqrt{169}\).

Step5: Find the square - root

\(\sqrt{169}=13\).

Answer:

13