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 coordinates of points A and B

Assume the coordinates of point A are \((x_1,y_1)\) and of point B are \((x_2,y_2)\). From the grid (counting units), if \(A=(3,4)\) and \(B=(7,7)\) (assuming standard grid - based coordinate reading where each square is 1 unit).

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute \(x_1 = 3,y_1 = 4,x_2 = 7,y_2 = 7\) into the formula:

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Another case: if \(A=(2,3)\) and \(B=(6,6)\) (assuming different grid - counting if the previous assumption was wrong).

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In general, for a right - triangle formed by the horizontal and vertical differences between the two points (where horizontal difference \(a\) and vertical difference \(b\) and the distance \(d\) is the hypotenuse), using the Pythagorean theorem \(a = 4\) (horizontal units between \(A\) and \(B\)), \(b=3\) (vertical units between \(A\) and \(B\)), \(d=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5\)

Answer:

\(5.00\) units