Question

1. the kite has vertices d(0, 3b), e(a, 0), and f(0, - 5b). what are the coordinates of g? (-a, 0) (0, -a) (a, 3b) (-a, 5b)

Explanation:

Step1: Recall kite - symmetry property

A kite is symmetric about one of its diagonals. In a kite with vertices \(D(0,3b)\), \(E(a,0)\), \(F(0, - 5b)\), the diagonal \(DF\) lies on the \(y\) - axis (\(x = 0\)). The other diagonal is perpendicular to \(DF\).

Step2: Analyze the symmetry of points about the \(y\) - axis

Points \(E(a,0)\) and \(G\) are symmetric about the \(y\) - axis. For a point \((x,y)\) symmetric about the \(y\) - axis, the new point has coordinates \((-x,y)\). Since \(E\) has coordinates \((a,0)\), the \(x\) - coordinate of \(G\) is \(-a\) and the \(y\) - coordinate is \(0\).

Answer:

A. \((-a,0)\)