Answer:
The coordinates of D are (8,3)
Step-by-step explanation:
We have quadrilateral ABCD being a parallelogram with coordinates A(3,2), B(5,4), C(10,5), and D(a,b).
We want to find the coordinates of D.
Since ABCD is a parallelogram, the diagonals AC and BD bisects each other.
The midpoint of AC is (13/2,7/2).
This is also the midpoint of BD.
By the midpoint rule:
[tex]( \frac{5 + a}{2} , \frac{4 + b}{2} ) = ( \frac{13}{2} , \frac{7}{2} )[/tex]
This implies that:
[tex]5 + a = 13 \\ a = 13 - 5 \\ a = 8[/tex]
Similarly,
[tex]4 + b = 7 \\ b = 7 - 4 \\ b = 3[/tex]
The coordinates of D are (8,3)
