Question

Use the Pythagorean Theorem to find the distance between these two points on the graph. Round your answer to the nearest tenth.
the two points are (-5, 5) and (2,-2)

Answer 1

To find the distance between the two points \((-5, 5)\) and \((2, -2)\) using the Pythagorean Theorem, we can follow these steps:

1. **Identify the coordinates**:
- Point 1: \((x_1, y_1) = (-5, 5)\)
- Point 2: \((x_2, y_2) = (2, -2)\)

2. **Calculate the differences in the x and y coordinates**:
\[
\Delta x = x_2 - x_1 = 2 - (-5) = 2 + 5 = 7
\]
\[
\Delta y = y_2 - y_1 = -2 - 5 = -7
\]

3. **Use the Pythagorean Theorem** to find the distance \(d\):
\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\]

Plugging in the values:
\[
d = \sqrt{(7)^2 + (-7)^2} = \sqrt{49 + 49} = \sqrt{98}
\]

4. **Calculate \(\sqrt{98}\)** and round to the nearest tenth:
\[
\sqrt{98} \approx 9.899
\]

Rounding to the nearest tenth, we get:
\[
d \approx 9.9
\]

Therefore, the distance between the two points is approximately **9.9**.