ABCD is a parallelogram where A is (4,2), B is (-6,1), and D is (-3,-4). Find the co-ordinates of C.
If you have a sketch, that should be simpler.
The properties of a parallelogram is such that the sides AB and CD are parallel, meaning that AB and CD have the same gradient.
Same for BC and AD; they have the same gradient.
So:
1. Find the gradient of AB. (this is also gradient of CD)
2. Find the gradient of AD. (this is also gradient of BC)
3. Find equation of line through D having gradient AB.
4. Find equation of line through B having gradient AD.
5. Solve simultaneously for those two lines. The intersection is where point C is.
There is a shorter, visual way using vectors, but this makes a diagram a must, if you cannot picture the points in your head.
Vector AB = (10, 1)
So, C + (10, 1) = (-3, -4)
So, C = (-3 -10, -4 -1) = (-13, -5)
Hello, euclid2!
If you make a sketch, you can "walk" your way to the answer.
Code:A B o(4,2) (-6,1)o : : : : : -6 : : : D -7 : C : o - - - + o - - - + (-3,-4)
We see that vertex is at the lower-left.
Going from to , we move: 6 units down and 7 units left.
Since , going from to , we do the same.
Starting at , move 6 units down a 7 units left.
Therefore, vertex is