Question

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

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