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: Identify coordinates of A and B

Assume each grid square is 1 unit. Let's find the horizontal and vertical distances between A and B. Suppose A is at \((x_1, y_1)\) and B is at \((x_2, y_2)\). From the grid, let's say the horizontal difference (\(\Delta x\)) is 5 units and vertical difference (\(\Delta y\)) is 3 units (we need to check the actual grid, but for example, if A is 5 right and 3 up from B, or vice versa).

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 \(\Delta x = 5\), \(\Delta y = 3\). Then \(d = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}\).

Step3: Calculate and round

\(\sqrt{34} \approx 5.83\) (since \(5.83^2 \approx 34\)).

Answer:

5.83