Question

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

Explanation:

Step1: Determine horizontal and vertical displacements

Assume the grid - squares have a side - length of 1. Count the horizontal displacement $x$ and vertical displacement $y$ between the two endpoints of the line. Let's say the horizontal displacement $x = 10$ and the vertical displacement $y = 6$.

Step2: Apply the distance formula

The distance $d$ between two points in a coordinate plane (or the length of the line segment) is given by the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 10$ and $y = 6$ into the formula: $d=\sqrt{10^{2}+6^{2}}=\sqrt{100 + 36}=\sqrt{136}$.

Answer:

D. $\sqrt{136}$