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 units between \(A\) and \(B\) (\(x - \)difference). Let's assume \(A=(x_1,y_1)\) and \(B=(x_2,y_2)\). From the grid, the horizontal distance \(a = 4\) units and the vertical distance \(b=6\) units.

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

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

Step3: Calculate the numerical value

\(\sqrt{52}\approx7.21\) (using a calculator, \(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx2\times3.6055 = 7.211\approx7.21\))

Answer:

\(7.21\)