Question

Quadrilateral ABCD is a parallelogram. Given this, fill in the coordinates below.

Answer 1

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:

$( \frac{5 + a}{2} , \frac{4 + b}{2} ) = ( \frac{13}{2} , \frac{7}{2} )$

This implies that:

$5 + a = 13 \\ a = 13 - 5 \\ a = 8$

Similarly,

$4 + b = 7 \\ b = 7 - 4 \\ b = 3$

The coordinates of D are (8,3)