The coordinates of the fourth vertex, H is; (-6.056, 7.302)
How to find the Coordinates of a Kite?
A kite has 4 sides and we know that a pair of diagonally opposite angles of a kite are said to be congruent.
We are given the coordinates of its' vertices as;
E(1,6), F(3,5), and G(4,-3).
The two diagonals are perpendicular;
Slope of EG = (-3 - 6)/(4 - 1)
Slope of EG = -9/5
Equation of line passing through G is;
y = mx + c
-3 = -9/5(4) + c
-15 = -36 + 15c
c = 51/15 = 17/5
y = (-9/5)x + 17/5 ------(1)
Equation of line passing through F is;
y = mx + c
6 = (5/9)(1) + c
54 = -9 + 9c
c = 7
y = (5/9)x + 7 -----(2)
Solving eq 1 and eq 2 simultaneously gives;
x = -1.528 and y = 6.151
If (a, b) are coordinates of vertex H, then;
(a + 3)/2 = -1.528 and (b + 5)/2 = 6.151
Thus;
a = -6.056 and b = 7.302
Read more about Kites coordinates at; https://brainly.com/question/27761176
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