Question

enter the correct answer that completes the sentence below. the distance from the origin to the point (-10,24) is (simplify your answer.)

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 \((-10,24)\). So \(x_1 = 0,y_1=0,x_2=-10,y_2 = 24\).

Step2: Substitute the values into the formula

Substitute into the formula: \(d=\sqrt{(-10 - 0)^2+(24 - 0)^2}=\sqrt{(- 10)^2+24^2}\).

Step3: Calculate the squares

\((-10)^2=100\) and \(24^2 = 576\). Then \(d=\sqrt{100 + 576}\).

Step4: Add the numbers inside the square - root

\(100+576 = 676\). So \(d=\sqrt{676}\).

Step5: Simplify the square - root

Since \(26\times26=676\), \(\sqrt{676}=26\).

Answer:

\(26\)