Question

what is the distance of this line? 8 12 sqrt{60} sqrt{136} 60

Explanation:

Step1: Determine horizontal and vertical distances

Assume the endpoints of the line segment. Let's say the horizontal distance \( \Delta x = 10\) (counting grid - squares) and the vertical distance \( \Delta y=6\) (counting grid - squares).

Step2: Apply the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(d=\sqrt{(\Delta x)^2+(\Delta y)^2}\). Substituting \(\Delta x = 10\) and \(\Delta y = 6\), we get \(d=\sqrt{10^{2}+6^{2}}=\sqrt{100 + 36}\).

Step3: Calculate the result

\(d=\sqrt{136}\)

Answer:

\(\sqrt{136}\)