Question

Use the image to answer the question.

A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9.

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

Answer 1

To find the length between the two points (3,2) and (7,8) using the Pythagorean Theorem, we can first determine the difference in the x-coordinates and the difference in the y-coordinates.

1. **Calculate the differences:**
- Difference in x-coordinates: \( x_2 - x_1 = 7 - 3 = 4 \)
- Difference in y-coordinates: \( y_2 - y_1 = 8 - 2 = 6 \)

2. **Apply the Pythagorean Theorem:**

The formula for the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the differences we calculated:
\[
d = \sqrt{(4)^2 + (6)^2}
\]
\[
d = \sqrt{16 + 36}
\]
\[
d = \sqrt{52}
\]
\[
d \approx 7.21
\]

So, the length between the two points (3,2) and (7,8) is approximately **7.21**, rounded to the nearest hundredth.