A(-2,4), B(5,6), C(12,4) and D(5,2)
Plotting these points on the coordinate plane yields a shape that looks like it is either a rhombus or a kite. To decide, we simply check the relationship between points...
To go from A to B... we must go 7 units to the right and then 2 units up.
To go from B to C... we must go 7 units right and then 2 units down
To go from C to D... we must go 7 units left and then 2 units down
To go from D to A... we must go 7 units left and then w units up.
Since the movement in ALL cases is left or right by 7 units and up or down by 2 units, the length of every segment is identical. And because plotting the points clearly shows us that the angles between the sides is not 90 degrees....
this is a rhombus.
