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