Use the image to answer the question.

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• (7,8).
• (3, 2)
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Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

1 answer

To find the distance between the two points \((7, 8)\) and \((3, 2)\), we can use the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Here, \((x_1, y_1) = (7, 8)\) and \((x_2, y_2) = (3, 2)\). We can substitute these values into the formula:

  1. Calculate \(x_2 - x_1\): \[ x_2 - x_1 = 3 - 7 = -4 \]

  2. Calculate \(y_2 - y_1\): \[ y_2 - y_1 = 2 - 8 = -6 \]

  3. Now, substitute these differences into the distance formula: \[ d = \sqrt{(-4)^2 + (-6)^2} \]

  4. Calculate the squares: \[ d = \sqrt{16 + 36} = \sqrt{52} \]

  5. Now calculate \(\sqrt{52}\): \[ d \approx 7.2111 \]

Rounding to the nearest hundredth, the distance \(d\) is approximately:

\[ d \approx 7.21 \]

Therefore, the length between the two points is 7.21.