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? How do I work this out?

Answer 1

check the picture below.

so, we know that 3.5, 2.5 is the midpoint of each diagonal, keeping in mind that, in a parallelogram, the diagonals bisect each other, namely, they cut each other in two equal halves.





`\bf \left( \cfrac{x+2}{2}~,~\cfrac{y+5}{2} \right)=\stackrel{midpoint}{(3.5,2.5)}\implies \begin{cases} \cfrac{x+2}{2}=3.5\\\\ x+2=7\\ \boxed{x=5}\\ ----------\\ \cfrac{y+5}{2}=2.5\\\\ y+5=5\\ \boxed{y=0} \end{cases}`





`\bf \left( \cfrac{x+8}{2}~,~\cfrac{y+8}{2} \right)=\stackrel{midpoint}{(3.5,2.5)}\implies \begin{cases} \cfrac{x+8}{2}=3.5\\\\ x+8=7\\ \boxed{x=-1}\\ ----------\\ \cfrac{y+8}{2}=2.5\\\\ y+8=5\\ \boxed{y=-3} \end{cases}`