Question

E (-2,3) F (0,4) G (2,3) Rhombus EFGH has the coordinates shown. Find the coordinates of point H.

Answer 1

H would be (0,2) if it is a Rhombus

Answer 2

Coordinates of point H is (0,2).

Explanation:

Given the co-ordinates of rhombus which are E (-2,3), F (0,4), G (2,3). We have to find the coordinate of point H.

let coordinate of point H are (a,b).

Now, as diagonals of rhombus bisect each other.

⇒ O is the mid-point of HF and EG.

Hence, by mid-point formula

`((0+a)/(2),(4+b)/(2))=((2-2)/(2),(3+3)/(2))\\\\((a)/(2),(4+b)/(2))=(0,3)`

⇒
`(a)/(2)=0`,
`(4+b)/(2)=3`

⇒
`a=0`,
`4+b=6`

⇒ (a,b)=(0,2)

Hence, coordinates of point H is (0,2).