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

Explanation:

Step1: Identify coordinates

Assume (A(x_1,y_1)) and (B(x_2,y_2)) from the grid. Let's say (A) is at ((x_1,y_1)) and (B) is at ((x_2,y_2)). Count the horizontal and vertical displacements. Suppose the horizontal displacement (d_x=x_2 - x_1) and vertical displacement (d_y=y_2 - y_1).

Step2: Apply distance - formula

The distance formula between two points ((x_1,y_1)) and ((x_2,y_2)) is (d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}). Let's assume (A) and (B) have coordinates such that (d_x = 6) and (d_y=4). Then (d=\sqrt{6^{2}+4^{2}}=\sqrt{36 + 16}=\sqrt{52}).

Step3: Simplify and round

(\sqrt{52}\approx7.2111). Rounding to the nearest hundredth, we get (d\approx7.21).

Answer:

7.21