Coordinate geometry

okay, so basically ABCD is a parallelogram even though is doesn't look like one because i did this diagram on paint

how can i find the coordinates of C?

Equation of AC: y= - 1/2x + 4

Equation of BD: y = 4x - 5

tried using distance formula, but didnt work because there were 2 unknowns..

CE=EA

-2, 5

-2, 5

er how did you get that answer? its correct btw.

CE=EA

er ya...i tried using distance formula...but couldn't get anywhere because there were 2 unknwons involved, the x and y coordinate of C..

can use vector

AE = EC

Let C be (h,k)

Midpoint of AC = [(h+6)/2 , (k+1)/2]

Midpoint of AC = E (2,3)

Therefore [(h+6)/2 , (k+1)/2] = (2, 3)

(h+6)/2 = 2

h+6 = 4

h = -2

(k+1)/2 = 3

k+1= 6

k = 5

Thus C = (-2,5)

Normally I won't answer if someone gave the correct solution already. Problem is they don't learn vectors in Sec 3.

the diagionals will intersect and bisect the diagionals...so the midpoint of A and C is E. That's the proporties of parallelogram.