Question

if A(3,7) B(9,10) C(10,6) D(4,3) use the midpoint formula to determine whether AC and BD are diagonals of the parallelogram

Answer 1

Midpoint formula is used to determine the exact center of a line.

If these two lines are diagonals of the parallelogram then their centers must be same.

Let us apply it on AC line first. A = (3, 7) C = (10, 6)

`(x,\text{ y) = }((3+10))/(2),\text{ }(7+6)/(2))=((13)/(2),\text{ }(13)/(2))\rightarrow\text{ Coordinates of the mid point on AC line}`
`(x,y)\text{ = (}(9+4)/(2),(10+3)/(2))=((13)/(2),(13)/(2))\rightarrow\text{ BD line coordinates}`