Question

Find the length of diagonal XU in the hexagon below. Round your solution to 2 decimal points

Answer 1

The length of diagonal XU is 6.40 units

Explanation:

* Lets explain how to find the distance between two points

- The rule of the distance between two points
`(x_(1),y_(1))`

and
`(x_(2),y_(2))` is:

`d=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

* 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
`(x_(1),y_(1))` = (2 , 2)

∴ The point
`(x_(2),y_(2))` = (-2 , 7)

∴
`x_(1)=2,x_(2)=-2`

∴
`y_(1)=2,y_(2)=7`

∵
`d=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

∴
`d=\sqrt{(-2-2)^(2)+(7-2)^(2)}=\sqrt{(-4)^(2)+(5)^(2)}=√(16+25)=√(41)`

∵
`√(41)=6.403124`

∴ d = 6.40

* The length of diagonal XU is 6.40 units