Answer:
The length of diagonal XU is 6.40 units
Step-by-step explanation:
* Lets explain how to find the distance between two points
- The rule of the distance between two points [tex](x_{1},y_{1})[/tex]
and [tex](x_{2},y_{2})[/tex] is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
* Lets solve the problem
-From the attached figure:
- The coordinates of the vertex X are (2 , 2)
- The coordinates of the vertex U are (-2 , 7)
∴ The point [tex](x_{1},y_{1})[/tex] = (2 , 2)
∴ The point [tex](x_{2},y_{2})[/tex] = (-2 , 7)
∴ [tex]x_{1}=2,x_{2}=-2[/tex]
∴ [tex]y_{1}=2,y_{2}=7[/tex]
∵ [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
∴ [tex]d=\sqrt{(-2-2)^{2}+(7-2)^{2}}=\sqrt{(-4)^{2}+(5)^{2}}=\sqrt{16+25}=\sqrt{41}[/tex]
∵ [tex]\sqrt{41}=6.403124[/tex]
∴ d = 6.40
* The length of diagonal XU is 6.40 units
