Question

exponents, polynomials, and radicals
using the pythagorean theorem to find distance on a grid
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 it be \(a\)) and vertical units (let it be \(b\)). From the grid, \(a = 6\) units and \(b=4\) units.

Step2: Apply the Pythagorean theorem

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

Step3: Calculate the square - root and round

\(\sqrt{52}\approx7.2111\). Rounding \(7.2111\) to the nearest hundredth gives \(7.21\).

Answer:

\(7.21\)