To determine the distance between the points [tex]\((-3, 5)\)[/tex] and [tex]\((-3, -9)\)[/tex], we can use the distance formula. The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a Cartesian plane is given by:
[tex]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Given the points [tex]\((x_1, y_1) = (-3, 5)\)[/tex] and [tex]\((x_2, y_2) = (-3, -9)\)[/tex], we can plug these coordinates into the formula:
1. First, calculate the difference in the [tex]\(x\)[/tex]-coordinates:
[tex]\[
x_2 - x_1 = -3 - (-3) = -3 + 3 = 0
\][/tex]
2. Next, calculate the difference in the [tex]\(y\)[/tex]-coordinates:
[tex]\[
y_2 - y_1 = -9 - 5 = -14
\][/tex]
3. Now, square both of these differences:
[tex]\[
(x_2 - x_1)^2 = 0^2 = 0
\][/tex]
[tex]\[
(y_2 - y_1)^2 = (-14)^2 = 196
\][/tex]
4. Add the squared differences:
[tex]\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 0 + 196 = 196
\][/tex]
5. Finally, take the square root of the sum to find the distance:
[tex]\[
\sqrt{196} = 14
\][/tex]
Thus, the distance between the points [tex]\((-3, 5)\)[/tex] and [tex]\((-3, -9)\)[/tex] is:
[tex]\[
14
\][/tex]
Therefore, the correct answer is:
D 14
