Respuesta :
Answer:
The coordinates of vertex D are (1,2).
Step-by-step explanation:
Let the coordinates of D are (a,b).
It is given that ABCD is a parallelogram and the vertices of the parallelogram are A(-2,4), B(1,3) and C(4,1).
According to the property of parallelogram, the diagonals of the parallelogram bisect each other.
AC and BD are diagonals of the parallelogram ABCD.
Midpoint formula:
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Using midpoint formula, the midpoint of AC is
[tex]Midpoint_{AC}=(\frac{-2+4}{2},\frac{4+1}{2})=(1,\frac{5}{2})[/tex]
Using midpoint formula, the midpoint of BD is
[tex]Midpoint_{BD}=(\frac{1+a}{2},\frac{3+b}{2})[/tex]
Midpoint of both diagonals is the intersection point of the diagonals.
[tex]Midpoint_{AC}=Midpoint_{BD}[/tex]
[tex](1,\frac{5}{2})=(\frac{1+a}{2},\frac{3+b}{2})[/tex]
On comparing both the sides we get
[tex]1=\frac{1+a}{2}[/tex]
[tex]2=1+a[/tex]
[tex]2-1=a[/tex]
[tex]1=a[/tex]
The value of a is 1.
[tex]\frac{5}{2}=\frac{3+b}{2}[/tex]
[tex]5=3+b[/tex]
[tex]5-3=b[/tex]
[tex]2=b[/tex]
The value of b is 2.
Therefore the coordinates of vertex D are (1,2).
