Asked by meme_master22160

Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.(1 point) Responses 2.65 2.65 4.58 4.58 5.39 5.39 29 29

Answers

Answered by GPT-4o mini
To find the length between the points \((2, 5)\) and \((7, 3)\), we can use the distance formula, which is derived from the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\).

Now, we will substitute the values:

\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]

Calculating the differences:

\[
d = \sqrt{(5)^2 + (-2)^2}
\]

Next, we square the differences:

\[
d = \sqrt{25 + 4}
\]

Now, add these values:

\[
d = \sqrt{29}
\]

Finally, we can calculate the square root:

\[
d \approx 5.385
\]

Rounding to the nearest hundredth, we have:

\[
d \approx 5.39
\]

Thus, the length between the points \((2, 5)\) and \((7, 3)\) is approximately **5.39**.

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