Super Urgent Geometry Test Tommorrow- Help Needed (1 Viewer)

[Focus is Key]

If a=(1,5), b=(4,2) and C=(2,-3) find the co-ordinates of d such that ABCD is a parallelogram.

The answer is (-1,0). I did it two different ways. One which got it wrong and another super long way that got it correct, although I know there must be a faster way. I need to do it quickly under test conditions.

 

[2xL]

Do the long way. From what I know, there is no "short way". Either do equal sides or parallel sides and use simultaneous. I think doing parallel sides would be fastest.

EDIT: Also draw out a diagram and mark approximately the points. It will give an idea as to where D should be and which lines are parallel.

 

[qrpw]

Easiest way is to just look at the diagram, plot the last point, and count.
So for example, draw the diagram, and you can see (1,5) and (4,2) are a pair of points which differ by 3 and 3.
Then you have (2,-3), so the last point has to be 3 up and 3 to the left, which is (-1, 0).
You'll understand what I mean if you draw it.

 

[Sy123]

There are 3 possible points D can take, remember that.

 

[Drongoski]

Let co-ords of D be (x,y)

Now mid-pt of BD = mid-pt of AC

Equating the x-coords of both mid-pts and the y-coords:

(x+4)/2 = (1+2)/2 ==> x = -1

(y+2)/2 = (5-3)/2 ==> y = 0

i.e. D is (-1,0)

 

[Focus is Key]

Wow, this is such a fast response. That's awesome Appreciate this sooo much