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 units

Explanation:

Step1: Identify coordinates of A and B

Let's assume the coordinates of point A are \((x_1, y_1)\) and point B are \((x_2, y_2)\). From the grid, if we consider the bottom - left corner of the grid as a reference, let's say point A is at \((2, 1)\) and point B is at \((7, 5)\) (we can count the number of units horizontally and vertically. The horizontal distance between A and B is \(7 - 2=5\) units and the vertical distance is \(5 - 1 = 4\) units).

Step2: Apply the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substituting \(x_1 = 2\), \(y_1=1\), \(x_2 = 7\), \(y_2 = 5\) into the formula, we get:
\(d=\sqrt{(7 - 2)^2+(5 - 1)^2}=\sqrt{5^2+4^2}=\sqrt{25 + 16}=\sqrt{41}\)

Step3: Calculate the numerical value and round

We know that \(\sqrt{41}\approx6.4031\). Rounding to the nearest hundredth, we look at the thousandth place. The digit in the thousandth place is 3, which is less than 5, so we round down. So \(\sqrt{41}\approx6.40\)

Answer:

\(6.40\)