Question

try it yourself! use the pythagorean theorem to find th

Explanation:

Step1: Identify right - triangle sides

Let the horizontal distance between the two points be $a$ and the vertical distance be $b$. Assume the two points are such that the horizontal displacement is the difference in $x$ - coordinates and the vertical displacement is the difference in $y$ - coordinates. If we consider the two points that form a right - triangle with the line segment between them as the hypotenuse, from the graph, we can see that if the horizontal distance (change in $x$) is $a = 5$ and the vertical distance (change in $y$) is $b = 5$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle with sides $a$, $b$ and hypotenuse $c$ is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 5$ and $b = 5$ into the formula: $c=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}=5\sqrt{2}$. But if we assume the correct horizontal and vertical displacements from the graph are $a=6$ and $b = 1$, then $c=\sqrt{6^{2}+1^{2}}=\sqrt{36 + 1}=\sqrt{37}$.

Answer:

$\sqrt{37}$