Question

Apply the Pythagorean theorem to find the length between the two point. Round your answer to the nearest hundredth
point A (7,6)
point B (3,1)

Answer 1

To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), we can use the distance formula derived from the Pythagorean theorem:

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

Given the points \( A(7, 6) \) and \( B(3, 1) \):

- \( x_1 = 7 \)
- \( y_1 = 6 \)
- \( x_2 = 3 \)
- \( y_2 = 1 \)

Now we can substitute these values into the distance formula:

\[
d = \sqrt{(3 - 7)^2 + (1 - 6)^2}
\]
\[
d = \sqrt{(-4)^2 + (-5)^2}
\]
\[
d = \sqrt{16 + 25}
\]
\[
d = \sqrt{41}
\]

Now, we can use a calculator to find the value of \( \sqrt{41} \):

\[
\sqrt{41} \approx 6.403124237
\]

Rounding this to the nearest hundredth:

\[
d \approx 6.40
\]

Thus, the distance between the two points \( A(7, 6) \) and \( B(3, 1) \) is approximately **6.40**.