Question

what is the length of the line? choose 1 answer: a $sqrt{119}$ b $sqrt{60}$ c $sqrt{17}$ d 13

Explanation:

Step1: Assume grid - based coordinates

Let's assume the endpoints of the line segment can be used to form a right - triangle with the grid lines. Count the horizontal and vertical displacements between the endpoints. Suppose the horizontal displacement (run) is $x$ and the vertical displacement (rise) is $y$.

Step2: Apply the Pythagorean theorem

The length $d$ of a line segment in a 2 - D plane is given by the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$. If we count the grid squares, assume $x = 4$ and $y = 1$. Then $d=\sqrt{4^{2}+1^{2}}=\sqrt{16 + 1}=\sqrt{17}$.

Answer:

C. $\sqrt{17}$