Question

1. find the distance between the two points using the pythagorean theorem. a. √82 b. √5 c. √26 d. √85

Explanation:

Step1: Identify horizontal and vertical distances

Count the horizontal and vertical units between the two points. Suppose the horizontal distance $a$ and vertical distance $b$. From the grid, if we assume the starting - point and ending - point, we find that the horizontal change is 1 unit and the vertical change is 9 units.

Step2: Apply Pythagorean theorem

The Pythagorean theorem for the distance $d$ between two points in a coordinate - plane is $d=\sqrt{a^{2}+b^{2}}$. Here, $a = 1$ and $b = 9$. Then $d=\sqrt{1^{2}+9^{2}}=\sqrt{1 + 81}=\sqrt{82}$.

Answer:

A. $\sqrt{82}$