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

From the grid, the horizontal distance \( \Delta x\) between \(A\) and \(B\) is \(4\) units, and the vertical distance \( \Delta y\) is \(3\) units.

Step2: Apply the distance formula

The distance formula is \(d=\sqrt{(\Delta x)^{2}+(\Delta y)^{2}}\). Substituting \(\Delta x = 4\) and \(\Delta y=3\), we get \(d=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5\).

Answer:

\(5.00\)