Question

HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other.

A. (1,-1)
B. (1,1)
C. (1,0)
D. (0,1)

Answer 1

C

Explanation:

Answer 2

`C) \:(1,0)`

Explanation:

1) Let's find the Midpoint of IK and the Midpoint of HJ, for if there is a bisection then the midpoint is the first thing to look for.

`M_(IK)=\left ( (4-2)/(2),(3-3)/(2) \right )=(1,0)\\M_(HJ)=\left ( (-2+4)/(2),(2-2)/(2) \right )=(1,0)`

2) Notice that both midpoints share the same value, which means the diagonals cross each other equally in two parts.

3) It is possible to show geometrically, that this is a parallelogram since both diagonals bisect each other indeed.