Question

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

Answer 1

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**.