The coordinates of parallelogram abcd are a(0, 0) , b(a, 0) , c(
,
), and d(c, b) .

the coordinates of the midpoint of ac are (
, b2 ).

the coordinates of the midpoint of bd are ( a+c2 ,
).

the midpoints of the diagonals have the same coordinates.

therefore, ac and bd bisect each other.

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.