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.
1 unit

Explanation:

Step1: Determine the horizontal and vertical distances

Count the horizontal units between \(A\) and \(B\) (let's say \(x\) - distance). Count the vertical units between \(A\) and \(B\) (let's say \(y\) - distance). Suppose the horizontal distance \(x = 6\) units and the vertical distance \(y=4\) units.

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

The distance \(d\) between two points is \(d=\sqrt{x^{2}+y^{2}}\). Substitute \(x = 6\) and \(y = 4\) into the formula: \(d=\sqrt{6^{2}+4^{2}}=\sqrt{36 + 16}=\sqrt{52}\).

Step3: Calculate the value and round

\(\sqrt{52}\approx7.21\) (using a calculator, \(\sqrt{52}\approx7.2111\), and rounding to the nearest hundredth).

Answer:

\(7.21\)