Question

ABCD is a parallelogram. A is the point (2,5), B is the point (8,8) and the diagonals intersect at (3.5, 2.5). What are the coordinates of C and D?

I can plot the points, find the length of a line and the midpoint of a line but I can't see how they apply here. I'm extremely confused. When I try to draw a sketch, the values don't seem to make sense. I think I'm doing something wrong...please help!

Answer 1

see explanation.

Explanation:

One of the properties of a parallelogram is that the diagonals bisect each other.
Let coordinates of `C and D` be `(x_c,y_c) and (x_d,y_d)`, respectively, as shown in the diagram.
Given coordinates of the midpoint `M=(3.5,2.5)`,
`=> (3.5,2.5)=((2+x_c)/2,(5+y_c)/2)`
`=> (x_c,y_c)=(5,0)`
Similarly,
`(3.5,2.5)=((8+x_d)/2, (8+y_d)/2)`
`=> (x_d,y_d)=(-1,-3)`

Footnotes : the two diagonals `AC and BD` bisect each other, which means `AM=MC, and BM=MD`.