Question

find the distance between the points a and b given below.
(that is, find the length of the segment connecting a and b.)
round your answer to the nearest hundredth.

Explanation:

Step1: Determine the horizontal and vertical distances

Count the horizontal and vertical units between points \(A\) and \(B\). The horizontal distance \(x = 3\) units and the vertical distance \(y=2\) units.

Step2: Apply the distance formula (derived from Pythagorean theorem)

The distance \(d\) between two points is \(d=\sqrt{x^{2}+y^{2}}\). Substitute \(x = 3\) and \(y = 2\) into the formula: \(d=\sqrt{3^{2}+2^{2}}=\sqrt{9 + 4}=\sqrt{13}\).

Step3: Calculate the numerical value

\(\sqrt{13}\approx3.61\) (rounded to the nearest hundredth).

Answer:

\(3.61\)