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 displacements

Assume the grid - squares have side - length 1. Count the horizontal displacement $x$ and vertical displacement $y$ between the two endpoints of the line. Suppose the horizontal displacement $x = 5$ and the vertical displacement $y = 6$.

Step2: Apply the distance formula

The distance $d$ between two points in a 2 - D plane is given by the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 5$ and $y = 6$ into the formula: $d=\sqrt{5^{2}+6^{2}}=\sqrt{25 + 36}=\sqrt{61}$.

Answer:

B. $\sqrt{61}$