Answer: The coordinates of D are (-5,2).
Step-by-step explanation:
Given : The coordinates of three points in the coordinate plane are A(-2,-3), B(5,-3), C(2,2).
Let the coordinates of vertex D be (x,y).
Since ABCD is an parallelogram , then
Mid point of AC = Mid point of BD [Diagonals of parallelogram,bisects each other.] (i)
Formula for mid point between line joining (a,b) and (c,d)= [tex](\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]
Mid point of AC = [tex](\dfrac{-2+2}{2},\dfrac{-3+2}{2})=(0,\dfrac{-1}{2})[/tex]
Mid point of BD = [tex](\dfrac{5+x}{2},\dfrac{-3+y}{2})[/tex]
From (i) , we have
[tex](\dfrac{5+x}{2},\dfrac{-3+y}{2})=(0,\dfrac{-1}{2})\\\\\Rightarrow\ \dfrac{5+x}{2}=0,\ \dfrac{-3+y}{2}=\dfrac{-1}{2}\\\\\Rightarrow\ x+5=0\ \ \ -3+y=-1\\\\\Rightarrow\ x= -5\ \ \ , \ y=2[/tex]
Hence, the coordinates of D are (-5,2).
