Answer:
AC = 11.4
Step-by-step explanation:
To find the length of segment AC, given the coordinates of the endpoints, we can use the distance formula:
[tex]\boxed{\begin{array}{l}\underline{\sf Distance \;Formula}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\;d\;\textsf{is the distance between two points.} \\\phantom{ww}\bullet\;\;\textsf{$(x_1,y_1)$ and $(x_2,y_2)$ are the two points.}\end{array}}[/tex]
Given that A(-2, 5) and C(9, 2), we can substitute the coordinates into the distance formula and solve for AC:
[tex]AC=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\\\AC=\sqrt{(9-(-2))^2+(2-5)^2}\\\\AC=\sqrt{(11)^2+(-3)^2}\phantom{dontcopy}\\\\AC=\sqrt{121+9}\\\\AC=\sqrt{(130}\\\\AC=11.40175425...\\\\AC = 11.4\; \sf (nearest\;tenth)[/tex]
Therefore, the length of AC is 11.4 units, rounded to the nearest tenth.
Additional Information
Figure ABCD is a rectangle. The diagonals of a rectangle are equal in length and bisect one another. So, as BE = 5.7, then DE = 5.7. This means that BD = 5.7 + 5.7 = 11.4, and so AC = 11.4, which confirms the length we found using the distance formula.
