Answer:
Coordinates of point H is (0,2).
Step-by-step 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
[tex](\frac{0+a}{2},\frac{4+b}{2})=(\frac{2-2}{2},\frac{3+3}{2})\\\\(\frac{a}{2},\frac{4+b}{2})=(0,3)[/tex]
⇒ [tex]\frac{a}{2}=0[/tex], [tex]\frac{4+b}{2}=3[/tex]
⇒ [tex]a=0[/tex], [tex]4+b=6[/tex]
⇒ (a,b)=(0,2)
Hence, coordinates of point H is (0,2).
