Question

what is the length of the line? choose 1 answer: a 8 b 12 c $sqrt{60}$ d $sqrt{136}$

Explanation:

Step1: Identify horizontal and vertical displacements

Assume each grid - square side is 1 unit. Count the horizontal displacement $x$ and vertical displacement $y$ of the line's endpoints. The horizontal displacement $x = 10$ and the vertical displacement $y = 6$.

Step2: Apply the distance formula

The length $d$ of a line segment with horizontal displacement $x$ and vertical displacement $y$ in a coordinate - like system (using the Pythagorean theorem) is given by $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 10$ and $y = 6$ into the formula: $d=\sqrt{10^{2}+6^{2}}=\sqrt{100 + 36}=\sqrt{136}$.

Answer:

D. $\sqrt{136}$