find the distance between the points $a$ and $b$ given below.\n(that is, find the length of the segment…

Explanation:

Step1: Identify horizontal and vertical distances

Count the grid units between points $A$ and $B$. The horizontal distance (run) is $6$ units, and the vertical distance (rise) is $4$ units.

Step2: Apply the Pythagorean theorem

The distance $d$ is the hypotenuse of a right triangle with legs $a=6$ and $b=4$. $$d = \sqrt{a^2 + b^2}$$

Step3: Substitute values and calculate

Substitute the identified values into the formula. $$d = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52}$$

Step4: Evaluate the square root

Calculate the numerical value and round to the nearest hundredth. $$d \approx 7.2111...$$

Answer:

7.21 units