Question

State True or False.
The points A(1, 2), B(4, 3), C(1, 0) and D(-2, -1) are the vertices of a parallelogram. “The midpoints of AC and BD are the same.”

• A. True
• B. False

Answer 1

The correct option is A

True

$\text{Midpoint of diagonal AC}=(\frac{1+1}{2},\frac{2+0}{2})=(\frac{2}{2},\frac{2}{2})$ = (1,1)
$\text{Midpoint of diagonal BD}=(\frac{4-2}{2},\frac{3-1}{2})=(\frac{2}{2},\frac{2}{2})$ = (1, 1)
The midpoints of AC and BD coincide. Hence the given statement is TRUE.