To find the length of the segment [tex]\(\overline{W X}\)[/tex] with endpoints [tex]\(W(2, -7)\)[/tex] and [tex]\(X(5, -4)\)[/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] is given by:
[tex]\[
\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
First, we identify the coordinates of the points:
- [tex]\(W\)[/tex] has coordinates [tex]\((2, -7)\)[/tex]
- [tex]\(X\)[/tex] has coordinates [tex]\((5, -4)\)[/tex]
We then calculate the differences in the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates:
[tex]\[
x_2 - x_1 = 5 - 2 = 3
\][/tex]
[tex]\[
y_2 - y_1 = -4 + 7 = 3
\][/tex]
Now, plug these values into the distance formula:
[tex]\[
\sqrt{(3)^2 + (3)^2} = \sqrt{9 + 9} = \sqrt{18}
\][/tex]
We can simplify [tex]\(\sqrt{18}\)[/tex]:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
\][/tex]
Therefore, the length of [tex]\(\overline{W X}\)[/tex] is [tex]\(3\sqrt{2}\)[/tex].
The correct answer is:
E. [tex]\(3\sqrt{2}\)[/tex]
