Question

what is the length of the line?
choose 1 answer:
a (sqrt{11})
b (sqrt{61})
c (8)
d (11)

Explanation:

Step1: Identify horizontal and vertical distances

Assume each grid square has side length 1. The horizontal distance (Δx) between the two endpoints is \( 5 \) (from column 3 to column 8), and the vertical distance (Δy) is \( 6 \) (from row 4 to row 10).

Step2: Apply the distance formula

The distance \( d \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Substituting \( \Delta x = 5 \) and \( \Delta y = 6 \), we get \( d = \sqrt{5^2 + 6^2} = \sqrt{25 + 36} = \sqrt{61} \).

Answer:

B. \(\sqrt{61}\)