To find the distance between the points [tex]\((-4, -8)\)[/tex] and [tex]\( (10, -8) \)[/tex], we use the distance formula.
The distance formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a plane is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, we have:
- [tex]\((x_1, y_1) = (-4, -8)\)[/tex]
- [tex]\((x_2, y_2) = (10, -8)\)[/tex]
First, we calculate the differences in the [tex]\( x \)[/tex]-coordinates and the [tex]\( y \)[/tex]-coordinates:
[tex]\[ x_2 - x_1 = 10 - (-4) = 10 + 4 = 14 \][/tex]
[tex]\[ y_2 - y_1 = -8 - (-8) = -8 + 8 = 0 \][/tex]
Now, substitute these differences into the distance formula:
[tex]\[ d = \sqrt{(14)^2 + (0)^2} \][/tex]
Simplify inside the square root:
[tex]\[ d = \sqrt{196 + 0} = \sqrt{196} \][/tex]
Finally, take the square root of 196:
[tex]\[ d = 14 \][/tex]
So, the distance between the points [tex]\((-4, -8)\)[/tex] and [tex]\( (10, -8) \)[/tex] is [tex]\( 14 \)[/tex] units.
