Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary

1. 29
2. 4.58
3. 2.65
4. 5.39

1 answer

To find the length between the points (2, 5) and (7, 3), we can use the Pythagorean Theorem, which states that:

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

Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\).

Now, we'll calculate the differences in the x and y coordinates:

\[ x_2 - x_1 = 7 - 2 = 5 \]

\[ y_2 - y_1 = 3 - 5 = -2 \]

Now we can plug these values into the formula:

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

Calculating the squares:

\[ (5)^2 = 25 \]

\[ (-2)^2 = 4 \]

Now add these together:

\[ c = \sqrt{25 + 4} = \sqrt{29} \]

Finally, calculating \(\sqrt{29}\):

\[ c \approx 5.385 \]

Rounding to the nearest hundredth gives us:

\[ c \approx 5.39 \]

So, the length between the points (2, 5) and (7, 3) is 5.39.

The correct answer is 4. 5.39.