Questions: Find the distance between the pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (8,2) and (2,10) The distance between the points is units. (Simplify your answer. Type an exact answer, using radicals as needed.)

Find the distance between the pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (8,2) and (2,10) The distance between the points is units. (Simplify your answer. Type an exact answer, using radicals as needed.)
Transcript text: Find the distance between the pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. \[ (8,2) \text { and }(2,10) \] The distance between the points is $\square$ units. (Simplify your answer. Type an exact answer, using radicals as needed.)
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Solution

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Solution Steps

Step 1: Calculate the difference in the x-coordinates

\(\Delta x = x_2 - x_1 = 2 - 8 = -6\)

Step 2: Calculate the difference in the y-coordinates

\(\Delta y = y_2 - y_1 = 10 - 2 = 8\)

Step 3: Apply the distance formula derived from the Pythagorean theorem

\(Distance = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{-6^2 + 8^2} = 10\)

Step 4: Round the result to 2 decimal places

\(Distance = 10\)

Final Answer:

The distance between the points \((8, 2)\) and \((2, 10)\) is approximately 10 units.

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