To solve this problem, we need to find the slope and length of the line segment [tex]\(\overline{WX}\)[/tex].
### Slope of [tex]\(\overline{WX}\)[/tex]
First, let's find the slope of [tex]\(\overline{WX}\)[/tex]. The formula to calculate the slope between two points [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of point [tex]\(W\)[/tex] are [tex]\((3, 2)\)[/tex] and the coordinates of point [tex]\(X\)[/tex] are [tex]\((7, 5)\)[/tex].
Plugging the coordinates into the slope formula, we get:
[tex]\[ \text{slope} = \frac{5 - 2}{7 - 3} = \frac{3}{4} \][/tex]
### Length of [tex]\(\overline{WX}\)[/tex]
Next, we calculate the length of [tex]\(\overline{WX}\)[/tex] using the distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ \text{length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Substituting the coordinates of [tex]\(W\)[/tex] and [tex]\(X\)[/tex], we have:
[tex]\[ \text{length} = \sqrt{(7 - 3)^2 + (5 - 2)^2} \][/tex]
[tex]\[ \text{length} = \sqrt{4^2 + 3^2} \][/tex]
[tex]\[ \text{length} = \sqrt{16 + 9} \][/tex]
[tex]\[ \text{length} = \sqrt{25} \][/tex]
[tex]\[ \text{length} = 5 \][/tex]
With these calculations, we find that the slope of [tex]\(\overline{WX}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex] and the length of [tex]\(\overline{WX}\)[/tex] is 5.
### Conclusion
So, the correct statement is:
D. The slope of [tex]\(\overline{W X}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex], and the length of [tex]\(\overline{W X}\)[/tex] is 5.
