Let's determine the distance between the points [tex]\((-7, -18)\)[/tex] and [tex]\((-7, 25)\)[/tex].
To do this, we use the distance formula, which is given by:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Given the points [tex]\((-7, -18)\)[/tex] and [tex]\((-7, 25)\)[/tex], we can label them as:
[tex]\[
(x_1, y_1) = (-7, -18)
\][/tex]
[tex]\[
(x_2, y_2) = (-7, 25)
\][/tex]
First, calculate the difference in the coordinates:
[tex]\[
x_2 - x_1 = -7 - (-7) = -7 + 7 = 0
\][/tex]
[tex]\[
y_2 - y_1 = 25 - (-18) = 25 + 18 = 43
\][/tex]
Now, substitute these differences into the distance formula:
[tex]\[
d = \sqrt{(0)^2 + (43)^2} = \sqrt{0 + 1849} = \sqrt{1849}
\][/tex]
Taking the square root of 1849 gives us:
[tex]\[
d = 43
\][/tex]
Thus, the distance between the points [tex]\((-7, -18)\)[/tex] and [tex]\((-7, 25)\)[/tex] is [tex]\(43\)[/tex] units. Therefore, the correct answer is:
43 units.
