To find the distance between the points [tex]\((-6, 2)\)[/tex] and [tex]\( (8, 10) \)[/tex] on a coordinate grid, we use the distance formula:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
First, let's identify our points:
[tex]\[
(x_1, y_1) = (-6, 2)
\][/tex]
[tex]\[
(x_2, y_2) = (8, 10)
\][/tex]
Next, we substitute these values into the distance formula:
1. Calculate [tex]\(x_2 - x_1\)[/tex]:
[tex]\[
x_2 - x_1 = 8 - (-6) = 8 + 6 = 14
\][/tex]
2. Calculate [tex]\(y_2 - y_1\)[/tex]:
[tex]\[
y_2 - y_1 = 10 - 2 = 8
\][/tex]
3. Now, square the differences:
[tex]\[
(x_2 - x_1)^2 = 14^2 = 196
\][/tex]
[tex]\[
(y_2 - y_1)^2 = 8^2 = 64
\][/tex]
4. Add these squared differences:
[tex]\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 196 + 64 = 260
\][/tex]
5. Finally, take the square root of this sum to find the distance:
[tex]\[
d = \sqrt{260}
\][/tex]
Thus, the distance between the points [tex]\((-6, 2)\)[/tex] and [tex]\( (8, 10) \)[/tex] on a coordinate grid is [tex]\(\sqrt{260}\)[/tex].
