Certainly! Let's find the distance between the two points A and B using the distance formula.
Points:
- Point A: \(\((-2, 4)\)\)
- Point B: \(\((7, -3)\)\)
Distance Formula:
The distance \(\( d \)\) between two points \(\((x_1, y_1)\)\) and \(\((x_2, y_2)\)\) on a coordinate plane is given by:
\(\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]\)
Step-by-Step Solution:
1. Identify the coordinates:
- Point A: \(\((x_1, y_1) = (-2, 4)\)\)
- Point B: \(\((x_2, y_2) = (7, -3)\)\)
2. Subtract the x-coordinates:
\(\[
x_2 - x_1 = 7 - (-2) = 7 + 2 = 9
\]\)
3. Subtract the y-coordinates:
\(\[
y_2 - y_1 = -3 - 4 = -7
\]\)
4. Square the differences:
\(\[
(x_2 - x_1)^2 = 9^2 = 81
\]\)
\(\[
(y_2 - y_1)^2 = (-7)^2 = 49
\]\)
5. Add the squared differences:
\(\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 81 + 49 = 130
\]\)
6. Take the square root of the sum:
\(\[
d = \sqrt{130} \approx 11.40175425099138
\]\)
Therefore, the distance between point A \(\((-2, 4)\)\) and point B \(\((7, -3)\)\) is approximately \(\(11.40175425099138\)\).
