To find the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in the coordinate plane, we can use the distance formula:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given the points [tex]\( (0, -1) \)[/tex] and [tex]\( (0, -11) \)[/tex], we will label these coordinates as:
[tex]\[ x_1 = 0, \, y_1 = -1 \][/tex]
[tex]\[ x_2 = 0, \, y_2 = -11 \][/tex]
Step-by-Step Solution:
1. Subtract the [tex]\(x\)[/tex]-coordinates:
[tex]\[ x_2 - x_1 = 0 - 0 = 0 \][/tex]
2. Subtract the [tex]\(y\)[/tex]-coordinates:
[tex]\[ y_2 - y_1 = -11 - (-1) = -11 + 1 = -10 \][/tex]
3. Substitute these differences into the distance formula:
[tex]\[ \text{Distance} = \sqrt{(0)^2 + (-10)^2} \][/tex]
4. Simplify the expression under the square root:
[tex]\[ \text{Distance} = \sqrt{0 + 100} = \sqrt{100} \][/tex]
5. Compute the square root of 100:
[tex]\[ \sqrt{100} = 10 \][/tex]
Therefore, the distance between the points [tex]\((0, -1)\)[/tex] and [tex]\((0, -11)\)[/tex] is [tex]\(10\)[/tex]. So the correct answer is:
10
