Question

On a coordinate plane, kite H I J K with diagonals is shown. Point H is at (negative 3, 1), point I is at (negative 3, 4), point J is at (0, 4), and point K is at (2, negative 1).
Which statement proves that quadrilateral HIJK is a kite?

HI ⊥ IJ, and m∠H = m∠J.
IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK.
IK intersects HJ at the midpoint of HJ at (−1.5, 2.5).
The slope of HK = Negative two-fifths and the slope of JK = Negative five-halves

Answer 1

The second statement. It shows IH = IJ = 3 and JK = HK = √29, so the quadrilateral has two pairs of adjacent congruent sides (HI = IJ and JK = KH), which is the definition of a kite.