Certainly! Let's find the distance between the points [tex]\((0, -8)\)[/tex] and [tex]\((-6, 0)\)[/tex] using the distance formula. The distance formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a coordinate plane is:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, the coordinates of the points are:
[tex]\( (x_1, y_1) = (0, -8) \)[/tex]
[tex]\( (x_2, y_2) = (-6, 0) \)[/tex]
Now, let's substitute these values into the distance formula step by step.
1. Calculate the difference in the [tex]\(x\)[/tex]-coordinates:
[tex]\[ x_2 - x_1 = -6 - 0 = -6 \][/tex]
2. Calculate the difference in the [tex]\(y\)[/tex]-coordinates:
[tex]\[ y_2 - y_1 = 0 - (-8) = 0 + 8 = 8 \][/tex]
3. Square the differences:
[tex]\[ (x_2 - x_1)^2 = (-6)^2 = 36 \][/tex]
[tex]\[ (y_2 - y_1)^2 = 8^2 = 64 \][/tex]
4. Sum these squared differences:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 36 + 64 = 100 \][/tex]
5. Take the square root of the sum to find the distance:
[tex]\[ d = \sqrt{100} = 10 \][/tex]
Therefore, the distance between the points [tex]\((0, -8)\)[/tex] and [tex]\((-6, 0)\)[/tex] is [tex]\(\boxed{10}\)[/tex].
