Question

Find the length of diagonal HJ. Round to the nearest hundredth.

Answer 1

The length of the diagonal HJ is 10.82 units

Explanation:

* Lets revise the rule of the distance between two points

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

`(x_(1),y_(1))` and
`(x_(2),y_(2))` are the two points

* Lets use this rule to find the length of the diagonal HJ

∵ The coordinates of point H are (-4 , 3)

∵ The coordinates of point J are (5 , -3)

∴
`x_(1)=-4` and
`x_(2)=5`

∴
`y_(1)=3` and
`y_(2)=-3`

- Lets find the length of the diagonal HJ by using the rule above

∴ HJ =
`\sqrt{(5-(-4))^(2)+(-3-3)^(2)}=\sqrt{(5+4)^(2)+(-6)^(2)}`

∴ HJ =
`\sqrt{(9)^(2)+36}=√(81+36)=√(117)=10.81665`

∴ HJ = 10.82

* The length of the diagonal HJ is 10.82 units