Question

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

Explanation:

Step1: Determine horizontal and vertical changes

Count the horizontal and vertical grid - unit changes between the two points. Let the horizontal change be $a$ and the vertical change be $b$. By counting on the grid, assume the horizontal change $a = 9$ and the vertical change $b = 2$.

Step2: Apply Pythagorean theorem

The distance $d$ between two points is given by $d=\sqrt{a^{2}+b^{2}}$. Substitute $a = 9$ and $b = 2$ into the formula: $d=\sqrt{9^{2}+2^{2}}=\sqrt{81 + 4}=\sqrt{85}$.

Answer:

D. $\sqrt{85}$